REAL is V65() V66() V67() V71() set
NAT is V65() V66() V67() V68() V69() V70() V71() Element of bool REAL
bool REAL is set
omega is V65() V66() V67() V68() V69() V70() V71() set
bool omega is set
[:NAT,REAL:] is set
bool [:NAT,REAL:] is set
bool (bool REAL) is set
COMPLEX is V65() V71() set
RAT is V65() V66() V67() V68() V71() set
INT is V65() V66() V67() V68() V69() V71() set
bool NAT is set
[:COMPLEX,COMPLEX:] is set
bool [:COMPLEX,COMPLEX:] is set
[:COMPLEX,REAL:] is set
bool [:COMPLEX,REAL:] is set
K380() is V167() TopStruct
the carrier of K380() is V65() V66() V67() set
1 is non empty ext-real positive non negative natural V51() real V63() V64() V65() V66() V67() V68() V69() V70() Element of NAT
[:1,1:] is set
bool [:1,1:] is set
[:[:1,1:],1:] is set
bool [:[:1,1:],1:] is set
[:[:1,1:],REAL:] is set
bool [:[:1,1:],REAL:] is set
[:REAL,REAL:] is set
[:[:REAL,REAL:],REAL:] is set
bool [:[:REAL,REAL:],REAL:] is set
2 is non empty ext-real positive non negative natural V51() real V63() V64() V65() V66() V67() V68() V69() V70() Element of NAT
[:2,2:] is set
[:[:2,2:],REAL:] is set
bool [:[:2,2:],REAL:] is set
K408() is V153() V167() L7()
R^1 is non empty strict TopSpace-like V167() TopStruct
{} is empty trivial V65() V66() V67() V68() V69() V70() V71() set
+infty is non empty ext-real positive non negative non real set
the carrier of R^1 is non empty V65() V66() V67() set
bool the carrier of R^1 is set
IRRAT is V65() V66() V67() Element of bool REAL
-infty is non empty ext-real non positive negative non real set
K292(-infty,+infty) is set
T is non empty non trivial set
ADTS T is non empty strict TopSpace-like anti-discrete TopStruct
cobool T is non empty Element of bool (bool T)
bool T is set
bool (bool T) is set
TopStruct(# T,(cobool T) #) is non empty strict TopStruct
the non empty non trivial set is non empty non trivial set
ADTS the non empty non trivial set is non empty non trivial strict TopSpace-like anti-discrete TopStruct
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed Element of bool the carrier of T
Int (Cl (Int A)) is open Element of bool the carrier of T
B is Element of bool the carrier of T
Int B is open Element of bool the carrier of T
Cl (Int B) is closed Element of bool the carrier of T
Int (Cl (Int B)) is open Element of bool the carrier of T
(Int (Cl (Int A))) /\ (Int (Cl (Int B))) is open Element of bool the carrier of T
A /\ B is Element of bool the carrier of T
Int (A /\ B) is open Element of bool the carrier of T
Cl (Int (A /\ B)) is closed Element of bool the carrier of T
Int (Cl (Int (A /\ B))) is open Element of bool the carrier of T
(Int A) /\ (Int B) is open Element of bool the carrier of T
Cl ((Int A) /\ (Int B)) is closed Element of bool the carrier of T
Int (Cl ((Int A) /\ (Int B))) is open Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed Element of bool the carrier of T
Int (Cl A) is open Element of bool the carrier of T
Cl (Int (Cl A)) is closed Element of bool the carrier of T
B is Element of bool the carrier of T
A \/ B is Element of bool the carrier of T
Cl (A \/ B) is closed Element of bool the carrier of T
Int (Cl (A \/ B)) is open Element of bool the carrier of T
Cl (Int (Cl (A \/ B))) is closed Element of bool the carrier of T
Cl B is closed Element of bool the carrier of T
Int (Cl B) is open Element of bool the carrier of T
Cl (Int (Cl B)) is closed Element of bool the carrier of T
(Cl (Int (Cl A))) \/ (Cl (Int (Cl B))) is closed Element of bool the carrier of T
(Cl A) \/ (Cl B) is closed Element of bool the carrier of T
Int ((Cl A) \/ (Cl B)) is open Element of bool the carrier of T
Cl (Int ((Cl A) \/ (Cl B))) is closed Element of bool the carrier of T
T is TopStruct
the carrier of T is set
bool the carrier of T is set
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed Element of bool the carrier of T
Int (Cl A) is open Element of bool the carrier of T
Int A is open Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
A is Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
{} T is empty trivial V65() V66() V67() V68() V69() V70() V71() open closed boundary nowhere_dense (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
Int A is open Element of bool the carrier of T
(Int A) ` is closed (T) Element of bool the carrier of T
the carrier of T \ (Int A) is set
Cl (A `) is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open Element of bool the carrier of T
(Int (Cl A)) ` is closed (T) Element of bool the carrier of T
the carrier of T \ (Int (Cl A)) is set
(Cl A) ` is open Element of bool the carrier of T
the carrier of T \ (Cl A) is set
Cl ((Cl A) `) is closed (T) Element of bool the carrier of T
Int (A `) is open Element of bool the carrier of T
Cl (Int (A `)) is closed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
Cl A is closed (T) Element of bool the carrier of T
(Cl A) ` is open Element of bool the carrier of T
the carrier of T \ (Cl A) is set
Int (A `) is open Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed (T) Element of bool the carrier of T
(Cl (Int A)) ` is open Element of bool the carrier of T
the carrier of T \ (Cl (Int A)) is set
(Int A) ` is closed (T) Element of bool the carrier of T
the carrier of T \ (Int A) is set
Int ((Int A) `) is open Element of bool the carrier of T
Cl (A `) is closed (T) Element of bool the carrier of T
Int (Cl (A `)) is open Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Int (Int (Cl A)) is open Element of bool the carrier of T
Int A is open Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Cl (Cl (Int A)) is closed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed (T) Element of bool the carrier of T
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed (T) Element of bool the carrier of T
T is TopStruct
the carrier of T is set
bool the carrier of T is set
T is TopStruct
the carrier of T is set
bool the carrier of T is set
T is TopSpace-like TopStruct
[#] T is non proper open closed dense (T) Element of bool the carrier of T
the carrier of T is set
bool the carrier of T is set
Int ([#] T) is open Element of bool the carrier of T
Cl ([#] T) is closed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
[#] T is non proper open closed dense (T) Element of bool the carrier of T
the carrier of T is set
bool the carrier of T is set
Int ([#] T) is open Element of bool the carrier of T
Cl ([#] T) is closed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
{} T is empty trivial V65() V66() V67() V68() V69() V70() V71() open closed boundary nowhere_dense closed_condensed open_condensed (T) Element of bool the carrier of T
the carrier of T is set
bool the carrier of T is set
Cl ({} T) is closed (T) Element of bool the carrier of T
Int (Cl ({} T)) is open Element of bool the carrier of T
Int ({} T) is empty trivial V65() V66() V67() V68() V69() V70() V71() open closed boundary nowhere_dense closed_condensed open_condensed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open Element of bool the carrier of T
(Cl A) ` is open Element of bool the carrier of T
the carrier of T \ (Cl A) is set
Cl ((Cl A) `) is closed (T) Element of bool the carrier of T
Int (A `) is open Element of bool the carrier of T
Cl (Int (A `)) is closed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
{} T is empty trivial V65() V66() V67() V68() V69() V70() V71() open closed boundary nowhere_dense closed_condensed open_condensed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is open_condensed Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
Int A is open Element of bool the carrier of T
Cl (Int A) is closed (T) Element of bool the carrier of T
(Int A) ` is closed (T) Element of bool the carrier of T
the carrier of T \ (Int A) is set
Int ((Int A) `) is open Element of bool the carrier of T
Cl (A `) is closed (T) Element of bool the carrier of T
Int (Cl (A `)) is open Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is closed_condensed Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
A is Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed (T) Element of bool the carrier of T
Int (Cl (Int A)) is open Element of bool the carrier of T
Cl (Int (Cl (Int A))) is closed (T) Element of bool the carrier of T
Cl (Int (Cl A)) is closed (T) Element of bool the carrier of T
Int (Cl (Int (Cl A))) is open Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open open_condensed Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open open_condensed Element of bool the carrier of T
Int A is open Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed closed_condensed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed closed_condensed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
A is Element of bool the carrier of T
A is Element of bool the carrier of T
A is Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Cl (Int (Cl A)) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
B is Element of bool the carrier of T
Cl B is closed (T) Element of bool the carrier of T
Int (Cl B) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Int B is open Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int B) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Cl (Cl B) is closed (T) Element of bool the carrier of T
Int (Cl (Cl B)) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl (Int A)) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
B is Element of bool the carrier of T
Int B is open Element of bool the carrier of T
Cl (Int B) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Cl B is closed (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Int (Cl B) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
Int (Int B) is open Element of bool the carrier of T
Cl (Int (Int B)) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
T is TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Fr A is Element of bool the carrier of T
Cl A is Element of bool the carrier of T
Int A is Element of bool the carrier of T
(Cl A) \ (Int A) is Element of bool the carrier of T
B is Element of bool the carrier of T
A is Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Fr A is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
(Cl A) \ (Int A) is Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
(Cl (Int A)) \ (Int (Cl A)) is Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
Int (A `) is open Element of bool the carrier of T
Cl (Int (A `)) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
(Cl (Int A)) /\ (Cl (Int (A `))) is closed (T) Element of bool the carrier of T
(Int A) \/ ((Cl (Int A)) /\ (Cl (Int (A `)))) is Element of bool the carrier of T
(Int A) \/ (Cl (Int A)) is Element of bool the carrier of T
Cl (A `) is closed (T) Element of bool the carrier of T
(Cl A) \/ (Int A) is Element of bool the carrier of T
(Int A) \/ (Fr A) is Element of bool the carrier of T
Cl (A `) is closed (T) Element of bool the carrier of T
(Cl (A `)) \/ (Int (A `)) is Element of bool the carrier of T
Fr (A `) is closed (T) Element of bool the carrier of T
(Cl (A `)) \ (Int (A `)) is Element of bool the carrier of T
(Int (A `)) \/ (Fr (A `)) is Element of bool the carrier of T
(A `) ` is Element of bool the carrier of T
the carrier of T \ (A `) is set
Int ((A `) `) is open Element of bool the carrier of T
Cl (Int ((A `) `)) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
(Cl (Int (A `))) /\ (Cl (Int ((A `) `))) is closed (T) Element of bool the carrier of T
(Int (A `)) \/ ((Cl (Int (A `))) /\ (Cl (Int ((A `) `)))) is Element of bool the carrier of T
(Int (A `)) \/ (Cl (Int (A `))) is Element of bool the carrier of T
(Cl A) ` is open Element of bool the carrier of T
the carrier of T \ (Cl A) is set
Cl ((Cl A) `) is closed (T) Element of bool the carrier of T
(Int (Cl A)) ` is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
the carrier of T \ (Int (Cl A)) is set
(Int A) ` is closed (T) Element of bool the carrier of T
the carrier of T \ (Int A) is set
((Int (Cl A)) `) ` is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
the carrier of T \ ((Int (Cl A)) `) is set
T is TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Fr A is Element of bool the carrier of T
Cl A is Element of bool the carrier of T
Int A is Element of bool the carrier of T
(Cl A) \ (Int A) is Element of bool the carrier of T
Int (Fr A) is Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
(T,A) is Element of bool the carrier of T
Fr A is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
(Cl A) \ (Int A) is Element of bool the carrier of T
Int (Fr A) is open Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
(Int (Cl A)) \ (Cl (Int A)) is Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
Cl (A `) is closed (T) Element of bool the carrier of T
Int (Cl (A `)) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
(Int (Cl A)) /\ (Int (Cl (A `))) is open Element of bool the carrier of T
Cl (Fr A) is closed (T) Element of bool the carrier of T
(Cl (Int A)) ` is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
the carrier of T \ (Cl (Int A)) is set
((Cl (Int A)) `) ` is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
the carrier of T \ ((Cl (Int A)) `) is set
(Int (Cl A)) \ (((Cl (Int A)) `) `) is Element of bool the carrier of T
(Int A) ` is closed (T) Element of bool the carrier of T
the carrier of T \ (Int A) is set
Int ((Int A) `) is open Element of bool the carrier of T
(Int ((Int A) `)) ` is closed (T) Element of bool the carrier of T
the carrier of T \ (Int ((Int A) `)) is set
(Int (Cl A)) \ ((Int ((Int A) `)) `) is Element of bool the carrier of T
(Int (Cl (A `))) ` is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
the carrier of T \ (Int (Cl (A `))) is set
(Int (Cl A)) \ ((Int (Cl (A `))) `) is Element of bool the carrier of T
((Int (Cl (A `))) `) ` is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
the carrier of T \ ((Int (Cl (A `))) `) is set
(Int (Cl A)) /\ (((Int (Cl (A `))) `) `) is open Element of bool the carrier of T
(Cl A) /\ (Cl (A `)) is closed (T) Element of bool the carrier of T
Int ((Cl A) /\ (Cl (A `))) is open Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
(T,A) is Element of bool the carrier of T
Fr A is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
(Cl A) \ (Int A) is Element of bool the carrier of T
Int (Fr A) is open Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
(T,A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Fr A is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
(Cl A) \ (Int A) is Element of bool the carrier of T
Int (Fr A) is open Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
(Int (Cl A)) \ (Cl (Int A)) is Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
(Int (Cl A)) \ (Cl (Int A)) is Element of bool the carrier of T
Int (Int (Cl A)) is open Element of bool the carrier of T
Int (Cl (Int A)) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
(T,A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Fr A is closed (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
(Cl A) \ (Int A) is Element of bool the carrier of T
Int (Fr A) is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
(Int (Cl A)) \ (Cl (Int A)) is Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
(Int (Cl A)) \ (Cl (Int A)) is Element of bool the carrier of T
Cl (Int (Cl A)) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
Cl (Cl (Int A)) is closed (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
(T,A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Fr A is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
(Cl A) \ (Int A) is Element of bool the carrier of T
Int (Fr A) is open Element of bool the carrier of T
(T,(T,A)) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Fr (T,A) is closed boundary nowhere_dense (T) Element of bool the carrier of T
Cl (T,A) is closed (T) Element of bool the carrier of T
Int (T,A) is open Element of bool the carrier of T
(Cl (T,A)) \ (Int (T,A)) is Element of bool the carrier of T
Int (Fr (T,A)) is empty trivial V65() V66() V67() V68() V69() V70() V71() open closed boundary nowhere_dense condensed closed_condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
(T,A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Fr A is closed (T) Element of bool the carrier of T
(Cl A) \ (Int A) is Element of bool the carrier of T
Int (Fr A) is open Element of bool the carrier of T
T is V65() V66() V67() Element of bool the carrier of R^1
Int T is V65() V66() V67() open Element of bool the carrier of R^1
A is ext-real V51() real set
].-infty,A.] is V65() V66() V67() Element of bool REAL
].-infty,A.[ is V65() V66() V67() Element of bool REAL
T ` is V65() V66() V67() Element of bool the carrier of R^1
the carrier of R^1 \ T is V65() V66() V67() set
].A,+infty.[ is V65() V66() V67() Element of bool REAL
Cl (T `) is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
[.A,+infty.[ is V65() V66() V67() Element of bool REAL
(Cl (T `)) ` is V65() V66() V67() open Element of bool the carrier of R^1
the carrier of R^1 \ (Cl (T `)) is V65() V66() V67() set
T is V65() V66() V67() Element of bool the carrier of R^1
Int T is V65() V66() V67() open Element of bool the carrier of R^1
A is ext-real V51() real set
[.A,+infty.[ is V65() V66() V67() Element of bool REAL
].A,+infty.[ is V65() V66() V67() Element of bool REAL
T ` is V65() V66() V67() Element of bool the carrier of R^1
the carrier of R^1 \ T is V65() V66() V67() set
].-infty,A.[ is V65() V66() V67() Element of bool REAL
Cl (T `) is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
].-infty,A.] is V65() V66() V67() Element of bool REAL
(Cl (T `)) ` is V65() V66() V67() open Element of bool the carrier of R^1
the carrier of R^1 \ (Cl (T `)) is V65() V66() V67() set
A is V65() V66() V67() Element of bool the carrier of R^1
Cl A is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
B is ext-real V51() real set
].-infty,B.] is V65() V66() V67() Element of bool REAL
A is ext-real V51() real set
IRRAT (B,A) is V65() V66() V67() Element of bool REAL
].-infty,B.] \/ (IRRAT (B,A)) is V65() V66() V67() Element of bool REAL
[.A,+infty.[ is V65() V66() V67() Element of bool REAL
(].-infty,B.] \/ (IRRAT (B,A))) \/ [.A,+infty.[ is V65() V66() V67() Element of bool REAL
T is V65() V66() V67() Element of bool the carrier of R^1
B is set
C is ext-real V51() real set
C is ext-real V51() real set
].B,A.[ is V65() V66() V67() open Element of bool REAL
IRRAT /\ ].B,A.[ is V65() V66() V67() Element of bool REAL
C is ext-real V51() real set
C is ext-real V51() real set
Cl T is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
T is V65() V66() V67() Element of bool the carrier of R^1
Int T is V65() V66() V67() open Element of bool the carrier of R^1
A is ext-real V51() real set
B is ext-real V51() real set
RAT (A,B) is V65() V66() V67() Element of bool REAL
T ` is V65() V66() V67() Element of bool the carrier of R^1
the carrier of R^1 \ T is V65() V66() V67() set
REAL \ T is V65() V66() V67() Element of bool REAL
].-infty,A.] is V65() V66() V67() Element of bool REAL
IRRAT (A,B) is V65() V66() V67() Element of bool REAL
].-infty,A.] \/ (IRRAT (A,B)) is V65() V66() V67() Element of bool REAL
[.B,+infty.[ is V65() V66() V67() Element of bool REAL
(].-infty,A.] \/ (IRRAT (A,B))) \/ [.B,+infty.[ is V65() V66() V67() Element of bool REAL
Cl (T `) is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
[#] R^1 is non empty non proper V65() V66() V67() open closed dense non boundary condensed closed_condensed open_condensed semi-open ( R^1 ) ( R^1 ) Element of bool the carrier of R^1
(Cl (T `)) ` is V65() V66() V67() open Element of bool the carrier of R^1
the carrier of R^1 \ (Cl (T `)) is V65() V66() V67() set
{} R^1 is empty trivial V65() V66() V67() V68() V69() V70() V71() open closed boundary nowhere_dense condensed closed_condensed open_condensed semi-open ( R^1 ) ( R^1 ) Element of bool the carrier of R^1
A is V65() V66() V67() Element of bool the carrier of R^1
Int A is V65() V66() V67() open Element of bool the carrier of R^1
B is ext-real V51() real set
A is ext-real V51() real set
IRRAT (B,A) is V65() V66() V67() Element of bool REAL
].B,A.[ is V65() V66() V67() open Element of bool REAL
IRRAT /\ ].B,A.[ is V65() V66() V67() Element of bool REAL
T is V65() V66() V67() Element of bool the carrier of R^1
A is ext-real V51() real set
T is ext-real V51() real set
IRRAT (T,A) is V65() V66() V67() Element of bool REAL
].T,A.[ is V65() V66() V67() open Element of bool REAL
IRRAT /\ ].T,A.[ is V65() V66() V67() Element of bool REAL
IRRAT /\ {} is V65() V66() V67() V68() V69() V70() Element of bool REAL
T is ext-real V51() real set
A is ext-real V51() real set
IRRAT (T,A) is V65() V66() V67() Element of bool REAL
[.T,+infty.[ is V65() V66() V67() Element of bool REAL
B is set
A is ext-real V51() real set
T is V65() V66() V67() Element of bool the carrier of R^1
Int T is V65() V66() V67() open Element of bool the carrier of R^1
A is ext-real V51() real set
].-infty,A.[ is V65() V66() V67() Element of bool REAL
B is ext-real V51() real set
A is ext-real V51() real set
RAT (B,A) is V65() V66() V67() Element of bool REAL
].-infty,A.[ \/ (RAT (B,A)) is V65() V66() V67() Element of bool REAL
[.A,B.] is V65() V66() V67() closed Element of bool REAL
IRRAT (B,A) is V65() V66() V67() Element of bool REAL
[.A,+infty.[ is V65() V66() V67() Element of bool REAL
T ` is V65() V66() V67() Element of bool the carrier of R^1
the carrier of R^1 \ T is V65() V66() V67() set
REAL \ (].-infty,A.[ \/ (RAT (B,A))) is V65() V66() V67() Element of bool REAL
REAL \ (RAT (B,A)) is V65() V66() V67() Element of bool REAL
(REAL \ (RAT (B,A))) \ ].-infty,A.[ is V65() V66() V67() Element of bool REAL
].-infty,B.] is V65() V66() V67() Element of bool REAL
].-infty,B.] \/ (IRRAT (B,A)) is V65() V66() V67() Element of bool REAL
(].-infty,B.] \/ (IRRAT (B,A))) \/ [.A,+infty.[ is V65() V66() V67() Element of bool REAL
((].-infty,B.] \/ (IRRAT (B,A))) \/ [.A,+infty.[) \ ].-infty,A.[ is V65() V66() V67() Element of bool REAL
(IRRAT (B,A)) \/ [.A,+infty.[ is V65() V66() V67() Element of bool REAL
].-infty,B.] \/ ((IRRAT (B,A)) \/ [.A,+infty.[) is V65() V66() V67() Element of bool REAL
(].-infty,B.] \/ ((IRRAT (B,A)) \/ [.A,+infty.[)) \ ].-infty,A.[ is V65() V66() V67() Element of bool REAL
].-infty,B.] \ ].-infty,A.[ is V65() V66() V67() Element of bool REAL
((IRRAT (B,A)) \/ [.A,+infty.[) \ ].-infty,A.[ is V65() V66() V67() Element of bool REAL
(].-infty,B.] \ ].-infty,A.[) \/ (((IRRAT (B,A)) \/ [.A,+infty.[) \ ].-infty,A.[) is V65() V66() V67() Element of bool REAL
[.A,B.] \/ (((IRRAT (B,A)) \/ [.A,+infty.[) \ ].-infty,A.[) is V65() V66() V67() Element of bool REAL
(IRRAT (B,A)) \ ].-infty,A.[ is V65() V66() V67() Element of bool REAL
[.A,+infty.[ \ ].-infty,A.[ is V65() V66() V67() Element of bool REAL
((IRRAT (B,A)) \ ].-infty,A.[) \/ ([.A,+infty.[ \ ].-infty,A.[) is V65() V66() V67() Element of bool REAL
[.A,B.] \/ (((IRRAT (B,A)) \ ].-infty,A.[) \/ ([.A,+infty.[ \ ].-infty,A.[)) is V65() V66() V67() Element of bool REAL
right_closed_halfline A is V65() V66() V67() closed Element of bool REAL
K290(A,+infty) is set
D is V65() V66() V67() Element of bool the carrier of R^1
Cl D is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
[.B,+infty.[ is V65() V66() V67() Element of bool REAL
B is V65() V66() V67() Element of bool the carrier of R^1
Cl B is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
[.A,B.] \/ ((IRRAT (B,A)) \/ [.A,+infty.[) is V65() V66() V67() Element of bool REAL
{A} is non empty trivial V65() V66() V67() Element of bool REAL
].A,+infty.[ is V65() V66() V67() Element of bool REAL
{A} \/ ].A,+infty.[ is non empty V65() V66() V67() Element of bool REAL
(IRRAT (B,A)) \/ ({A} \/ ].A,+infty.[) is non empty V65() V66() V67() Element of bool REAL
[.A,B.] \/ ((IRRAT (B,A)) \/ ({A} \/ ].A,+infty.[)) is non empty V65() V66() V67() Element of bool REAL
[.A,B.] \/ (IRRAT (B,A)) is V65() V66() V67() Element of bool REAL
([.A,B.] \/ (IRRAT (B,A))) \/ ({A} \/ ].A,+infty.[) is non empty V65() V66() V67() Element of bool REAL
([.A,B.] \/ (IRRAT (B,A))) \/ [.A,+infty.[ is V65() V66() V67() Element of bool REAL
Cl (T `) is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
C is V65() V66() V67() Element of bool the carrier of R^1
B \/ C is V65() V66() V67() Element of bool the carrier of R^1
Cl (B \/ C) is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
(Cl (B \/ C)) \/ (Cl D) is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
Cl C is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
(Cl B) \/ (Cl C) is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
((Cl B) \/ (Cl C)) \/ (Cl D) is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
[.B,A.] is V65() V66() V67() closed Element of bool REAL
B \/ [.B,A.] is V65() V66() V67() set
(B \/ [.B,A.]) \/ D is V65() V66() V67() set
[.A,A.] is V65() V66() V67() closed Element of bool REAL
[.A,A.] \/ D is V65() V66() V67() set
[.A,+infty.[ is V65() V66() V67() Element of bool REAL
(Cl (T `)) ` is V65() V66() V67() open Element of bool the carrier of R^1
the carrier of R^1 \ (Cl (T `)) is V65() V66() V67() set
A is ext-real V51() real set
T is ext-real V51() real set
[.T,A.] is V65() V66() V67() closed Element of bool REAL
{A} is non empty trivial V65() V66() V67() Element of bool REAL
[.T,A.] \/ {A} is non empty V65() V66() V67() Element of bool REAL
[.T,A.[ is V65() V66() V67() Element of bool REAL
[.T,A.[ \/ {A} is non empty V65() V66() V67() Element of bool REAL
([.T,A.[ \/ {A}) \/ {A} is non empty V65() V66() V67() Element of bool REAL
A is ext-real V51() real set
T is ext-real V51() real set
].-infty,T.[ is V65() V66() V67() Element of bool REAL
[.T,A.] is V65() V66() V67() closed Element of bool REAL
].-infty,T.[ \/ [.T,A.] is V65() V66() V67() Element of bool REAL
].A,+infty.[ is V65() V66() V67() Element of bool REAL
(].-infty,T.[ \/ [.T,A.]) \/ ].A,+infty.[ is V65() V66() V67() Element of bool REAL
{T} is non empty trivial V65() V66() V67() Element of bool REAL
REAL \ {T} is V65() V66() V67() Element of bool REAL
(REAL \ {T}) \/ {T} is non empty V65() V66() V67() Element of bool REAL
].T,+infty.[ is V65() V66() V67() Element of bool REAL
].-infty,T.[ \/ ].T,+infty.[ is V65() V66() V67() Element of bool REAL
(].-infty,T.[ \/ ].T,+infty.[) \/ {T} is non empty V65() V66() V67() Element of bool REAL
].T,+infty.[ \/ {T} is non empty V65() V66() V67() Element of bool REAL
].-infty,T.[ \/ (].T,+infty.[ \/ {T}) is non empty V65() V66() V67() Element of bool REAL
[.T,+infty.[ is V65() V66() V67() Element of bool REAL
].-infty,T.[ \/ [.T,+infty.[ is V65() V66() V67() Element of bool REAL
[.A,+infty.[ is V65() V66() V67() Element of bool REAL
[.T,A.] \/ [.A,+infty.[ is V65() V66() V67() Element of bool REAL
].-infty,T.[ \/ ([.T,A.] \/ [.A,+infty.[) is V65() V66() V67() Element of bool REAL
{A} is non empty trivial V65() V66() V67() Element of bool REAL
{A} \/ ].A,+infty.[ is non empty V65() V66() V67() Element of bool REAL
[.T,A.] \/ ({A} \/ ].A,+infty.[) is non empty V65() V66() V67() Element of bool REAL
].-infty,T.[ \/ ([.T,A.] \/ ({A} \/ ].A,+infty.[)) is non empty V65() V66() V67() Element of bool REAL
[.T,A.] \/ {A} is non empty V65() V66() V67() Element of bool REAL
([.T,A.] \/ {A}) \/ ].A,+infty.[ is non empty V65() V66() V67() Element of bool REAL
].-infty,T.[ \/ (([.T,A.] \/ {A}) \/ ].A,+infty.[) is non empty V65() V66() V67() Element of bool REAL
].-infty,T.[ \/ ([.T,A.] \/ {A}) is non empty V65() V66() V67() Element of bool REAL
(].-infty,T.[ \/ ([.T,A.] \/ {A})) \/ ].A,+infty.[ is non empty V65() V66() V67() Element of bool REAL
T is V65() V66() V67() Element of bool the carrier of R^1
Int T is V65() V66() V67() open Element of bool the carrier of R^1
A is ext-real V51() real set
].-infty,A.] is V65() V66() V67() Element of bool REAL
B is ext-real V51() real set
A is ext-real V51() real set
[.B,A.] is V65() V66() V67() closed Element of bool REAL
].-infty,A.] \/ [.B,A.] is V65() V66() V67() Element of bool REAL
].-infty,A.[ is V65() V66() V67() Element of bool REAL
].B,A.[ is V65() V66() V67() open Element of bool REAL
].-infty,A.[ \/ ].B,A.[ is V65() V66() V67() Element of bool REAL
].A,+infty.[ is V65() V66() V67() Element of bool REAL
].A,+infty.[ is V65() V66() V67() Element of bool REAL
].A,+infty.[ /\ ].A,+infty.[ is V65() V66() V67() Element of bool REAL
].A,B.[ is V65() V66() V67() open Element of bool REAL
B is V65() V66() V67() Element of bool the carrier of R^1
Cl B is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
[.A,B.] is V65() V66() V67() closed Element of bool REAL
C is V65() V66() V67() Element of bool the carrier of R^1
Cl C is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
[.A,+infty.[ is V65() V66() V67() Element of bool REAL
T ` is V65() V66() V67() Element of bool the carrier of R^1
the carrier of R^1 \ T is V65() V66() V67() set
REAL \ (].-infty,A.] \/ [.B,A.]) is V65() V66() V67() Element of bool REAL
left_closed_halfline A is V65() V66() V67() closed Element of bool REAL
K291(-infty,A) is set
REAL \ (left_closed_halfline A) is V65() V66() V67() Element of bool REAL
(REAL \ (left_closed_halfline A)) \ [.B,A.] is V65() V66() V67() Element of bool REAL
right_open_halfline A is V65() V66() V67() open Element of bool REAL
K292(A,+infty) is set
(right_open_halfline A) \ [.B,A.] is V65() V66() V67() Element of bool REAL
[.B,+infty.[ is V65() V66() V67() Element of bool REAL
[.B,+infty.[ \ ].A,+infty.[ is V65() V66() V67() Element of bool REAL
].A,+infty.[ \ ([.B,+infty.[ \ ].A,+infty.[) is V65() V66() V67() Element of bool REAL
].A,+infty.[ \ [.B,+infty.[ is V65() V66() V67() Element of bool REAL
].A,+infty.[ /\ ].A,+infty.[ is V65() V66() V67() Element of bool REAL
(].A,+infty.[ \ [.B,+infty.[) \/ (].A,+infty.[ /\ ].A,+infty.[) is V65() V66() V67() Element of bool REAL
].A,B.[ \/ ].A,+infty.[ is V65() V66() V67() Element of bool REAL
Cl (T `) is V65() V66() V67() closed ( R^1 ) Element of bool the carrier of R^1
(Cl (T `)) ` is V65() V66() V67() open Element of bool the carrier of R^1
the carrier of R^1 \ (Cl (T `)) is V65() V66() V67() set
[.A,+infty.[ \/ [.A,B.] is V65() V66() V67() Element of bool REAL
REAL \ ([.A,+infty.[ \/ [.A,B.]) is V65() V66() V67() Element of bool REAL
right_closed_halfline A is V65() V66() V67() closed Element of bool REAL
K290(A,+infty) is set
REAL \ (right_closed_halfline A) is V65() V66() V67() Element of bool REAL
(REAL \ (right_closed_halfline A)) \ [.A,B.] is V65() V66() V67() Element of bool REAL
left_open_halfline A is V65() V66() V67() open Element of bool REAL
K292(-infty,A) is set
(left_open_halfline A) \ [.A,B.] is V65() V66() V67() Element of bool REAL
T is set
A is set
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
A is Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
(T,A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Fr A is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
(Cl A) \ (Int A) is Element of bool the carrier of T
Int (Fr A) is open Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
(Int (Cl A)) \ (Cl (Int A)) is Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) Element of bool the carrier of T
(Int (Cl A)) \ (Cl (Int A)) is Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
(T,A) is open condensed open_condensed semi-open (T) (T) Element of bool the carrier of T
Fr A is closed (T) Element of bool the carrier of T
Cl A is closed (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
(Cl A) \ (Int A) is Element of bool the carrier of T
Int (Fr A) is open Element of bool the carrier of T
A is Element of bool the carrier of T
(T,A) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Fr A is closed (T) (T) (T) (T) Element of bool the carrier of T
Cl A is closed (T) (T) (T) (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
(Cl A) \ (Int A) is Element of bool the carrier of T
Int (Fr A) is open Element of bool the carrier of T
T is non empty TopSpace-like anti-discrete TopStruct
the carrier of T is non empty set
bool the carrier of T is set
A is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl A is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
T is non empty non trivial strict TopSpace-like anti-discrete TopStruct
the carrier of T is non empty non trivial set
bool the carrier of T is set
the Element of the carrier of T is Element of the carrier of T
{ the Element of the carrier of T} is non empty trivial proper (T) (T) (T) Element of bool the carrier of T
B is Element of bool the carrier of T
Cl B is closed (T) (T) (T) (T) Element of bool the carrier of T
the non empty non trivial strict TopSpace-like anti-discrete TopStruct is non empty non trivial strict TopSpace-like anti-discrete TopStruct
the carrier of the non empty non trivial strict TopSpace-like anti-discrete TopStruct is non empty non trivial set
bool the carrier of the non empty non trivial strict TopSpace-like anti-discrete TopStruct is set
the ( the non empty non trivial strict TopSpace-like anti-discrete TopStruct ) ( the non empty non trivial strict TopSpace-like anti-discrete TopStruct ) ( the non empty non trivial strict TopSpace-like anti-discrete TopStruct ) Element of bool the carrier of the non empty non trivial strict TopSpace-like anti-discrete TopStruct is ( the non empty non trivial strict TopSpace-like anti-discrete TopStruct ) ( the non empty non trivial strict TopSpace-like anti-discrete TopStruct ) ( the non empty non trivial strict TopSpace-like anti-discrete TopStruct ) Element of bool the carrier of the non empty non trivial strict TopSpace-like anti-discrete TopStruct
{} the non empty non trivial strict TopSpace-like anti-discrete TopStruct is empty trivial V65() V66() V67() V68() V69() V70() V71() open closed boundary nowhere_dense condensed closed_condensed open_condensed semi-open ( the non empty non trivial strict TopSpace-like anti-discrete TopStruct ) ( the non empty non trivial strict TopSpace-like anti-discrete TopStruct ) ( the non empty non trivial strict TopSpace-like anti-discrete TopStruct ) ( the non empty non trivial strict TopSpace-like anti-discrete TopStruct ) ( the non empty non trivial strict TopSpace-like anti-discrete TopStruct ) Element of bool the carrier of the non empty non trivial strict TopSpace-like anti-discrete TopStruct
].-infty,1.[ is V65() V66() V67() Element of bool REAL
4 is non empty ext-real positive non negative natural V51() real V63() V64() V65() V66() V67() V68() V69() V70() Element of NAT
RAT (2,4) is V65() V66() V67() Element of bool REAL
].-infty,1.[ \/ (RAT (2,4)) is V65() V66() V67() Element of bool REAL
C is V65() V66() V67() Element of bool the carrier of R^1
Cl C is V65() V66() V67() closed ( R^1 ) ( R^1 ) ( R^1 ) ( R^1 ) Element of bool the carrier of R^1
[.2,4.] is V65() V66() V67() closed Element of bool REAL
B is V65() V66() V67() Element of bool the carrier of R^1
Cl B is V65() V66() V67() closed ( R^1 ) ( R^1 ) ( R^1 ) ( R^1 ) Element of bool the carrier of R^1
].-infty,1.] is V65() V66() V67() Element of bool REAL
A is V65() V66() V67() Element of bool the carrier of R^1
Cl A is V65() V66() V67() closed ( R^1 ) ( R^1 ) ( R^1 ) ( R^1 ) Element of bool the carrier of R^1
].-infty,1.] \/ [.2,4.] is V65() V66() V67() Element of bool REAL
Int (Cl A) is V65() V66() V67() open condensed open_condensed semi-open ( R^1 ) ( R^1 ) ( R^1 ) ( R^1 ) ( R^1 ) Element of bool the carrier of R^1
].2,4.[ is V65() V66() V67() open Element of bool REAL
].-infty,1.[ \/ ].2,4.[ is V65() V66() V67() Element of bool REAL
Int A is V65() V66() V67() open Element of bool the carrier of R^1
Cl (Int A) is V65() V66() V67() closed condensed closed_condensed semi-open ( R^1 ) ( R^1 ) ( R^1 ) ( R^1 ) ( R^1 ) Element of bool the carrier of R^1
3 is non empty ext-real positive non negative natural V51() real V63() V64() V65() V66() V67() V68() V69() V70() Element of NAT
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
{} T is empty trivial V65() V66() V67() V68() V69() V70() V71() open closed boundary nowhere_dense condensed closed_condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
T is TopSpace-like () TopStruct
the carrier of T is set
bool the carrier of T is set
T is TopSpace-like () TopStruct
the carrier of T is set
bool the carrier of T is set
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
Cl (A `) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (A `)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int (A `) is open Element of bool the carrier of T
Cl (Int (A `)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
(Int A) ` is closed (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Int A) is set
Int ((Int A) `) is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Cl (Int A)) ` is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Cl (Int A)) is set
Cl A is closed (T) (T) (T) (T) Element of bool the carrier of T
(Cl A) ` is open Element of bool the carrier of T
the carrier of T \ (Cl A) is set
Cl ((Cl A) `) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Int (Cl A)) ` is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Int (Cl A)) is set
Cl A is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Cl (Int A)) ` is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Cl (Int A)) is set
(Int (Cl A)) ` is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Int (Cl A)) is set
(Int A) ` is closed (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Int A) is set
Int ((Int A) `) is open Element of bool the carrier of T
(Cl A) ` is open Element of bool the carrier of T
the carrier of T \ (Cl A) is set
Cl ((Cl A) `) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (A `) is open Element of bool the carrier of T
Cl (Int (A `)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (A `) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (A `)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
B is Element of bool the carrier of T
B ` is Element of bool the carrier of T
the carrier of T \ B is set
Int (B `) is open Element of bool the carrier of T
Cl (Int (B `)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (B `) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (B `)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int B is open Element of bool the carrier of T
(Int B) ` is closed (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Int B) is set
Int ((Int B) `) is open Element of bool the carrier of T
Cl (Int B) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Cl (Int B)) ` is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Cl (Int B)) is set
Cl B is closed (T) (T) (T) (T) Element of bool the carrier of T
(Cl B) ` is open Element of bool the carrier of T
the carrier of T \ (Cl B) is set
Cl ((Cl B) `) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl B) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Int (Cl B)) ` is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Int (Cl B)) is set
(A `) ` is Element of bool the carrier of T
the carrier of T \ (A `) is set
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
Cl A is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Int (Cl A)) ` is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Int (Cl A)) is set
(Cl A) ` is open Element of bool the carrier of T
the carrier of T \ (Cl A) is set
Cl ((Cl A) `) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (A `) is open Element of bool the carrier of T
Cl (Int (A `)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Cl (Int (A `))) ` is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Cl (Int (A `))) is set
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Cl (Int A)) ` is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Cl (Int A)) is set
(Int A) ` is closed (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Int A) is set
Int ((Int A) `) is open Element of bool the carrier of T
Cl (A `) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (A `)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Int (Cl (A `))) ` is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
the carrier of T \ (Int (Cl (A `))) is set
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is (T) (T) (T) Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
T is TopSpace-like () TopStruct
the carrier of T is set
bool the carrier of T is set
A is (T) (T) (T) Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
T is TopSpace-like () TopStruct
the carrier of T is set
bool the carrier of T is set
A is (T) (T) (T) Element of bool the carrier of T
A ` is Element of bool the carrier of T
the carrier of T \ A is set
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (Int A)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (Int (Cl A)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (Cl (Int A)) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Int (Cl A)) is open Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (Int A)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (Int (Cl A)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
Cl A is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
B is Element of bool the carrier of T
Cl B is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl B) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Int (Cl A)) /\ (Int (Cl B)) is open Element of bool the carrier of T
A /\ B is Element of bool the carrier of T
Cl (A /\ B) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (A /\ B)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int B is open Element of bool the carrier of T
Cl (Int B) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Cl (Int A)) \/ (Cl (Int B)) is closed (T) (T) (T) (T) Element of bool the carrier of T
A \/ B is Element of bool the carrier of T
Int (A \/ B) is open Element of bool the carrier of T
Cl (Int (A \/ B)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (Int (Cl B)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (Int (Cl A)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (A \/ B) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (A \/ B)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (Int (Cl (A \/ B))) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Cl A) /\ (Cl B) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int ((Cl A) /\ (Cl B)) is open Element of bool the carrier of T
(Int A) \/ (Int B) is open Element of bool the carrier of T
Cl ((Int A) \/ (Int B)) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (Int B)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int (A /\ B) is open Element of bool the carrier of T
Cl (Int (A /\ B)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (Int (A /\ B))) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (Int A)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
T is TopSpace-like TopStruct
the carrier of T is set
bool the carrier of T is set
A is Element of bool the carrier of T
B is Element of bool the carrier of T
A \/ B is Element of bool the carrier of T
A /\ B is Element of bool the carrier of T
Int A is open Element of bool the carrier of T
Cl (Int A) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl A is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl A) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (Int (Cl A)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl B is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl B) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int B is open Element of bool the carrier of T
Cl (Int B) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (Int B)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (Int A)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (Int (Cl B)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int (A \/ B) is open Element of bool the carrier of T
Cl (Int (A \/ B)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Cl (Int A)) \/ (Cl (Int B)) is closed (T) (T) (T) (T) Element of bool the carrier of T
Cl (A \/ B) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (A \/ B)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (Int (Cl (A \/ B))) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Cl (A /\ B) is closed (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (A /\ B)) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
(Int (Cl A)) /\ (Int (Cl B)) is open Element of bool the carrier of T
Int (A /\ B) is open Element of bool the carrier of T
Cl (Int (A /\ B)) is closed condensed closed_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T
Int (Cl (Int (A /\ B))) is open condensed open_condensed semi-open (T) (T) (T) (T) (T) Element of bool the carrier of T