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
  F is open iff COMPLEMENT(F) is closed
proof
  F = COMPLEMENT COMPLEMENT F;
  hence thesis by Th9;
end;
