
theorem Th19:
  for S, T being TopSpace st S, T are_homeomorphic holds Omega S,
  Omega T are_isomorphic
proof
  let S, T be TopSpace;
  assume S,T are_homeomorphic;
  then consider h being Function of S, T such that
A1: h is being_homeomorphism;
A2: the carrier of T = the carrier of Omega T by Lm1;
  the carrier of S = the carrier of Omega S by Lm1;
  then reconsider f = h as Function of Omega S, Omega T by A2;
  take f;
  thus thesis by A1,Th18;
end;
