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

theorem
  A is F_sigma & B is F_sigma implies A /\ B is F_sigma
proof
  assume that
A1: A is F_sigma and
A2: B is F_sigma;
  consider F being closed countable Subset-Family of T such that
A3: A = union F by A1;
  consider G being closed countable Subset-Family of T such that
A4: B = union G by A2;
  reconsider H = INTERSECTION (F,G) as Subset-Family of T;
A5: H is closed by Th21;
  card H c= card [:F,G:] & [:F,G:] is countable by Th25,CARD_4:7;
  then
A6: H is countable by WAYBEL12:1;
  A /\ B = union H by A3,A4,SETFAM_1:28;
  hence thesis by A5,A6;
end;
