reserve X for non empty TopSpace,
  D for Subset of X;

theorem
  for X being non empty TopSpace holds (for A being Subset of X holds (A
  <> {} implies A is dense)) implies X is anti-discrete
proof
  let X be non empty TopSpace;
  assume
A1: for A being Subset of X holds (A <> {} implies A is dense);
   for A being Subset of X st A is non empty holds Cl A = the carrier of X
       by A1,TOPS_3:def 2;
  hence thesis by Th11;
end;
