Definition:Isolated Point (Metric Space)/Space

Definition
Let $M = \left({A, d}\right)$ be a metric space. $a \in A$ is an isolated point of $M$ there exists an open $\epsilon$-ball of $x$ containing no points other than $a$:
 * $\exists \epsilon \in \R_{>0}: B_\epsilon \left({a}\right) = \left\{{a}\right\}$

That is:
 * $\exists \epsilon \in \R_{>0}: \left\{{x \in A: d \left({x, a}\right) < \epsilon}\right\} = \left\{{a}\right\}$