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