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

theorem Th63:
  { KurExSet, KurExSet` } misses Kurat14OpPart KurExSet
proof
  set A = KurExSet;
  assume { A, A` } meets Kurat14OpPart A;
  then consider x being object such that
A1: x in { A, A` } and
A2: x in Kurat14OpPart A by XBOOLE_0:3;
  reconsider x as Subset of R^1 by A2;
  x = A or x = A` by A1,TARSKI:def 2;
  then
A3: x` = A by A2,TOPS_2:def 1;
  x is open by A2,TOPS_2:def 1;
  hence thesis by A3;
end;
