reserve T for non empty TopSpace,
  A, B for Subset of T,
  F, G for Subset-Family of T;

theorem
  for T being set, F being Subset-Family of T st F is
  closed_for_countable_unions holds {} in F
proof
  let T be set, F be Subset-Family of T;
  reconsider E = {} as countable Subset-Family of T by XBOOLE_1:2;
A1: E c= F;
  assume F is closed_for_countable_unions;
  hence thesis by A1,ZFMISC_1:2;
end;
