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 closed implies F \ G is closed
proof
  assume
A1: F is closed;
  let P;
  assume P in F \ G;
  then P in F by XBOOLE_0:def 5;
  hence thesis by A1;
end;
