reserve A, B, X, Y for set;
reserve R, S, T for non empty TopSpace;

theorem
  [:S,T:], [:T,S:] are_homeomorphic
proof
  reconsider f = <:pr2(the carrier of S,the carrier of T), pr1(the carrier of
  S,the carrier of T):> as Function of [:S,T:], [:T,S:] by Th42;
  take f;
  thus thesis by Th43;
end;
