reserve T for TopSpace;
reserve T for non empty TopSpace;
reserve F for Subset-Family of T;
reserve T for non empty TopSpace;

theorem Th75:
  for F being Subset-Family of T holds F is closed-domains-family
  implies Cl(union F) is closed_condensed & Cl Int(meet F) is closed_condensed
proof
  let F be Subset-Family of T;
  assume F is closed-domains-family;
  then F is domains-family by Th72;
  then Cl(union F) = Cl Int Cl(union F) by Th65;
  hence Cl(union F) is closed_condensed by TOPS_1:def 7;
  thus thesis by TDLAT_1:22;
end;
