reserve T1,T2,T3 for TopSpace,
  A1 for Subset of T1, A2 for Subset of T2, A3 for Subset of T3;

theorem
  A1,A2 are_homeomorphic implies A2,A1 are_homeomorphic
proof
  assume A1,A2 are_homeomorphic;
  then T1|A1,T2|A2 are_homeomorphic by METRIZTS:def 1;
  hence A2,A1 are_homeomorphic by METRIZTS:def 1;
end;
