intro X; exists (closure X).
exists (union X (complement (closure X))).
split; auto.
split; auto.
apply Lemma1.
Qed.
Definition nbh := neighbour.
Definition clopen (X : Top) := open X /\ closed X.

Lemma clopenbasis : forall (f : B) (n : nat), clopen (nbh f n).
intros f n.