Definition:Isolated Point (Topology)/Subset/Definition 1

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 $H$ :
 * $\exists U \in \tau: U \cap H = \left\{{x}\right\}$

That is, there exists an open set of $T$ containing no points of $H$ other than $x$.

Also see

 * Equivalence of Definitions of Isolated Point