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

theorem Th10:
  Cl KurExSet = {1} \/ [. 2,+infty .[
proof
  set A = KurExSet;
  reconsider B = {1}, C = RAT (2,4) \/ ]. 4, 5 .[ \/ ]. 5,+infty .[ as Subset
  of R^1 by TOPMETR:17;
  A = {1} \/ (RAT (2,4) \/ ]. 4, 5 .[ \/ ]. 5,+infty .[) by XBOOLE_1:113;
  then
A1: Cl A = Cl B \/ Cl C by PRE_TOPC:20;
  Cl B = {1} by BORSUK_5:38;
  hence thesis by A1,BORSUK_5:56;
end;
