reserve X for non empty TopSpace;

theorem Th4:
  for A being empty Subset of X holds A is not maximal_T_0
proof
  consider a being object such that
A1: a in the carrier of X by XBOOLE_0:def 1;
  reconsider a as Point of X by A1;
  let A be empty Subset of X;
  now
    take C = {a};
    thus C is T_0 & A c= C & A <> C by TSP_1:12,XBOOLE_1:2;
  end;
  hence thesis;
end;
