
theorem Th14:
  for S, T being non empty TopSpace st S, T are_homeomorphic & S
  is compact holds T is compact
proof
  let S, T be non empty TopSpace;
  assume that
A1: S, T are_homeomorphic and
A2: S is compact;
  consider f being Function of S, T such that
A3: f is being_homeomorphism by A1;
  f is continuous & rng f = [#] T by A3;
  hence thesis by A2,COMPTS_1:14;
end;
