reserve x, y for set,
  T for TopStruct,
  GX for TopSpace,
  P, Q, M, N for Subset of T,
  F, G for Subset-Family of T,
  W, Z for Subset-Family of GX,
  A for SubSpace of T;
reserve S for non empty TopStruct,
  f for Function of T, S,
  H for Subset-Family of S;

theorem
  f is being_homeomorphism implies f" is being_homeomorphism
by Th49,Th50,Th51;
