reserve T for non empty TopSpace,
  A, B for Subset of T,
  F, G for Subset-Family of T,
  x for set;

theorem Th40:
  for T being TopSpace holds Der {}T = {}T
proof
  let T be TopSpace;
    Cl {}T is empty;
    then {} = {}T \/ Der {}T by Th29
      .= Der {}T;
    hence thesis;
end;
