Definition:Isolated Point (Topology)/Subset/Definition 2

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $H \subseteq S$ be a subset of $S$.

$x \in H$ is an isolated point of $H$ $x$ is not a limit point of $H$.

That is, $x$ is not in the derived set of $H$.

Also see

 * Equivalence of Definitions of Isolated Point