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

theorem
  for A being Subset of R^1, a, b being Real st A = RAT (a,b)
  holds Int A = {}
proof
  let A be Subset of R^1, a, b be Real;
  assume
A1: A = RAT (a,b);
  A` = REAL \ A by TOPMETR:17
    .= ]. -infty,a.] \/ IRRAT (a,b) \/ [.b,+infty .[ by A1,BORSUK_5:58;
  then Cl A` = [#]R^1 by Th27;
  then (Cl A`)` = {}R^1 by XBOOLE_1:37;
  hence thesis by TOPS_1:def 1;
end;
