reserve Y for TopStruct;
reserve X for non empty TopSpace;

theorem Th40:
  for A being empty Subset of X holds A is not maximal_discrete
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 discrete & A c= C & A <> C by Th30,XBOOLE_1:2;
  end;
  hence thesis;
end;
