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 Cl
  A = A) implies X is discrete
proof
  let X be non empty TopSpace;
  assume
A1: for A being Subset of X holds Cl A = A;
  now
    let A be Subset of X;
    Cl A = A by A1;
    hence A is closed;
  end;
  hence thesis by TDLAT_3:16;
end;
