Isolated Point in Metric Space iff Isolated Point in Topological Space

Theorem
Let $M = \struct{A, d}$ be a metric space.

Let $T = \struct{A, \tau}$ be the topological space with the topology induced by $d$.

Let $H \subseteq A$.

Then:
 * $x \in H$ is an isolated point in $M$ $x$ is an isolated point in $T$