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

theorem Th46:
  for T being TopSpace st T is T_1 holds T is T_1/2
proof
  let T be TopSpace;
  assume
A1: T is T_1;
  for A being Subset of T holds Der A is closed
  proof
    let A be Subset of T;
    Der A = Cl Der A by A1,TOPGEN_1:33;
    hence thesis;
  end;
  hence thesis;
end;
