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

theorem Th40:
  Cl KurExSet <> KurExSet
proof
  set A = KurExSet;
  ( not 5 in {1})& not 5 in RAT (2, 4) by BORSUK_5:29,TARSKI:def 1;
  then ( not 5 in ]. 4, 5 .[)& not 5 in {1} \/ RAT (2, 4) by XBOOLE_0:def 3
,XXREAL_1:4;
  then
A1: ( not 5 in ]. 5,+infty .[)& not 5 in {1} \/ RAT (2, 4) \/ ]. 4, 5 .[ by
XBOOLE_0:def 3,XXREAL_1:235;
  5 in [. 2,+infty .[ by XXREAL_1:236;
  then 5 in Cl A by Th10,XBOOLE_0:def 3;
  hence thesis by A1,XBOOLE_0:def 3;
end;
