reserve T for TopSpace,
  x, y, a, b, U, Ux, rx for set,
  p, q for Rational,
  F, G for Subset-Family of T,
  Us, I for Subset-Family of Sorgenfrey-line;

theorem Th6: :: following TOPGEN_5:42
  for A being Subset of real-anti-diagonal
    holds A is closed Subset of Sorgenfrey-plane
proof
   reconsider B = real-anti-diagonal as closed Subset of
     Sorgenfrey-plane by Th4;
   let A be Subset of real-anti-diagonal;
   A c= B;
   then reconsider A as Subset of Sorgenfrey-plane by XBOOLE_1:1;
   Der A c= Der B by TOPGEN_1:30;
   then Der A c= {} by Th5;
   then Der A = {};
   then Cl A = A \/ {} by TOPGEN_1:29;
   hence thesis;
end;
