Let a be an element of A. Prove that A is an isolated point of A iff there exists an epsilon neighborhood V(a) such that V(a)intersectA={a}

A point is an isolated point if it is not a limit point.

Let a be an element of A.

Let be an isolated point. We want to show V(a)intersectA={a}.

Since a is not a limit point, we say x=liman satisfying an=x