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

theorem Th82:
  for F being Subset-Family of T holds F is open-domains-family
  implies Int(meet F) is open_condensed & Int Cl(union F) is open_condensed
proof
  let F be Subset-Family of T;
  assume F is open-domains-family;
  then F is domains-family by Th79;
  then Int Cl Int(meet F) = Int(meet F) by Th66;
  hence Int(meet F) is open_condensed by TOPS_1:def 8;
  thus thesis by TDLAT_1:23;
end;
