:: ISOMICHI semantic presentation

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 /\