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;

theorem Th25:
  Q is open implies for P being Subset of A st P=Q holds P is open
proof
  assume
A1: Q is open;
  let P be Subset of A;
  assume P=Q;
  then Q /\ [#] A = P by XBOOLE_1:28;
  hence thesis by A1,Th24;
end;
