theorem
  A is a_neighborhood of a implies NTop2Top A is a_neighborhood of NTop2Top a
  proof
    reconsider T = NTop2Top NT as non empty TopSpace;
    reconsider TA = NTop2Top A as Subset of T;
    reconsider Tx = NTop2Top a as Point of T;
    assume A is a_neighborhood of a;
    then a is_interior_point_of A;
    then a in Int A;
    then Tx in Int TA by Th34;
    hence thesis by CONNSP_2:def 1;
  end;
