reserve i for Integer,
  a, b, r, s for Real;

theorem
  for S, T being non empty TopSpace, f being Function of S,T st f is
  one-to-one onto holds f is open iff f" is continuous
proof
  let S, T be non empty TopSpace, f be Function of S,T such that
A1: f is one-to-one;
  assume f is onto;
  then
A2: rng f = [#]T;
  then rng (f") = [#]S by A1,TOPS_2:49;
  then
A3: f" is onto;
  f" is one-to-one & f"" = f by A1,A2,TOPS_2:50,51;
  hence thesis by A3,Th13;
end;
