reserve T for TopSpace,
  A, B for Subset of T;

theorem Th13: :: Remark 2
  A is regular_open implies A` is regular_closed
proof
  assume A is regular_open;
  then Int Cl A = A by TOPS_1:def 8;
  then Cl (Cl A)` = A` by TDLAT_3:2;
  then Cl Int (A`) = A` by TDLAT_3:3;
  hence thesis by TOPS_1:def 7;
end;
