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

theorem Th16:
  KurExSet` = ]. -infty, 1 .[ \/ ]. 1, 2 .] \/ IRRAT(2,4) \/ {4} \/ {5}
proof
  set A = KurExSet;
  reconsider B = {1}, C = RAT (2,4) \/ ]. 4, 5 .[ \/ ]. 5,+infty .[ as Subset
  of R^1 by TOPMETR:17;
A1: C` = ]. -infty, 2 .] \/ IRRAT(2,4) \/ {4} \/ {5} by BORSUK_5:60;
  A = {1} \/ (RAT (2,4) \/ ]. 4, 5 .[ \/ ]. 5,+infty .[) & B` = ]. -infty,
  1 .[ \/ ]. 1,+infty .[ by BORSUK_5:61,XBOOLE_1:113;
  hence thesis by A1,BORSUK_5:62,XBOOLE_1:53;
end;
