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

theorem
  A is G_delta implies A` is F_sigma
proof
  assume A is G_delta;
  then consider F being open countable Subset-Family of T such that
A1: A = meet F;
  per cases;
  suppose
A2: F <> {};
    set G = COMPLEMENT F;
A3: G is closed by TOPS_2:10;
    (meet F)` = union COMPLEMENT F by A2,TOPS_2:7;
    hence thesis by A1,A3;
  end;
  suppose
    F = {};
    then A` = [#]T by A1,SETFAM_1:1;
    hence thesis;
  end;
end;
