reserve T,T1,T2,S for non empty TopSpace;

theorem
  for S, T being non empty TopSpace, f being Function of S, T st f is
  being_homeomorphism holds f" is open
proof
  let S, T be non empty TopSpace, f be Function of S, T;
  assume f is being_homeomorphism;
  then
A1: rng f = [#] T & f is one-to-one continuous by TOPS_2:def 5;
  let P be Subset of T;
  f"P = (f").:P by A1,TOPS_2:55;
  hence thesis by A1,TOPS_2:43;
end;
