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

theorem
  Int Cl KurExSet <> Cl KurExSet
proof
  set A = KurExSet;
  1 in {1} by TARSKI:def 1;
  then 1 in Cl A by Th10,XBOOLE_0:def 3;
  hence thesis by Th26,XXREAL_1:235;
end;
