reserve T for TopSpace,
  A, B for Subset of T;

theorem
  for A being Subset of R^1, a, b being Real st A = IRRAT (a,b)
  holds Int A = {}
proof
  reconsider B = IRRAT as Subset of R^1 by TOPMETR:17;
  let A be Subset of R^1, a, b be Real;
  assume A = IRRAT (a,b);
  then A = IRRAT /\ ]. a, b .[ by BORSUK_5:def 3;
  then A c= B by XBOOLE_1:17;
  then A is boundary by TOPGEN_1:54,TOPS_3:11;
  hence thesis;
end;
