
theorem
  for S, T, V being non empty TopSpace st S, T are_homeomorphic & T, V
  are_homeomorphic holds S, V are_homeomorphic
proof
  let S, T, V be non empty TopSpace;
  assume that
A1: S, T are_homeomorphic and
A2: T, V are_homeomorphic;
  consider f being Function of S, T such that
A3: f is being_homeomorphism by A1;
  consider g being Function of T, V such that
A4: g is being_homeomorphism by A2;
  g * f is being_homeomorphism by A3,A4,TOPS_2:57;
  hence thesis;
end;
