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

theorem Th36:
  T is T_1 & A is dense-in-itself implies Cl A is dense-in-itself
proof
  assume
A1: T is T_1;
  assume A is dense-in-itself;
  then A c= Der A;
  then
A2: Der A = A \/ Der A by XBOOLE_1:12
    .= Cl A by Th29;
  Der Cl A = Der (A \/ Der A) by Th29
    .= Der A \/ Der Der A by Th31
    .= Cl A by A1,A2,Th32,XBOOLE_1:12;
  hence thesis;
end;
