reserve T for non empty TopSpace;
reserve A for Subset of T;

theorem Th60:
  card (Kurat14OpPart KurExSet) = 6
proof
  set A = KurExSet;
A1: ( not 5 in ]. -infty, 1 .[)& not 5 in ]. 1, 2 .[ by XXREAL_1:4;
  (Cl A)` = ]. -infty, 1 .[ \/ ]. 1, 2 .[ & 5 in (Cl (Cl (Cl A`)`)`)` by Th10
,Th22,BORSUK_5:63,XXREAL_1:235;
  then
A2: (Cl A)` <> (Cl (Cl (Cl A`)`)`)` by A1,XBOOLE_0:def 3;
A3: (Cl (Cl (Cl A)`)`)` = ]. -infty, 2 .[ by Th14,TOPMETR:17,XXREAL_1:224,294;
  6 in ]. 5,+infty .[ by XXREAL_1:235;
  then 6 in (Cl A`)` by Th18,XBOOLE_0:def 3;
  then
A4: (Cl (Cl (Cl A)`)`)` <> (Cl A`)` by A3,XXREAL_1:233;
A5: 4 in (Cl (Cl A)`)` by Th13,XXREAL_1:235;
  ( not 5 in ]. 4, 5 .[)& not 5 in ]. 5,+infty .[ by XXREAL_1:4;
  then
A6: not 5 in (Cl A`)` by Th18,XBOOLE_0:def 3;
  (Cl A)` <> (Cl Int Cl A)` by Th29,BORSUK_5:71;
  then
A7: (Cl A)` <> (Cl (Cl (Cl A)`)`)` by TOPS_1:def 1;
A8: not 5 in (Cl (Cl A`)`)` by Th20,XXREAL_1:233;
  (Cl (Cl (Cl A`)`)`)` = ]. 4,+infty .[ by Th21,TOPMETR:17,XXREAL_1:224,288;
  then
A9: (Cl (Cl A)`)` <> (Cl (Cl (Cl A`)`)`)` by A5,XXREAL_1:235;
  (Cl Int Cl A)` = (Cl (Cl (Cl A)`)`)` & (Cl Int A)` = (Cl (Cl A`)`)` by
TOPS_1:def 1;
  then
A10: (Cl (Cl (Cl A)`)`)` <> (Cl (Cl A`)`)` by Th31,BORSUK_5:71;
A11: ( not 5 in (Cl (Cl (Cl A)`)`)`)& 5 in (Cl (Cl (Cl A`)`)`)` by Th15,Th22,
XXREAL_1:233,235;
  (Cl (Cl A)`)` <> (Cl (Cl (Cl A)`)`)` by A3,A5,XXREAL_1:233;
  then (Cl A)`, (Cl (Cl A)`)`, (Cl (Cl (Cl A)`)`)`, (Cl A`)`, (Cl (Cl A`)`)`,
  (Cl (Cl (Cl A`)`)`)` are_mutually_distinct by A2,A7,A9,A4,A10,A6,A11,A8;
  hence thesis by BORSUK_5:3;
end;
