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

theorem Th41:
  KurExSet <> Int KurExSet
proof
  set A = KurExSet;
  1 in { 1 } by TARSKI:def 1;
  then 1 in {1} \/ RAT (2,4) by XBOOLE_0:def 3;
  then 1 in {1} \/ RAT (2,4) \/ ]. 4, 5 .[ by XBOOLE_0:def 3;
  then
A1: 1 in A by XBOOLE_0:def 3;
  Int A = ]. 4, 5 .[ \/ ]. 5,+infty .[ by Th18,TOPS_1:def 1;
  hence thesis by A1,XXREAL_1:223;
end;
