- #1

- 598

- 0

## Homework Statement

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)[tex]\cap[/tex]A={a}

## Homework Equations

## The Attempt at a Solution

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)[tex]\cap[/tex]A={a}.

Since a is not a limit point, we say x=lim[tex]a_{n}[/tex] satisfying [tex]a_{n}[/tex]=x