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

Definition
Let $T = \struct {S, \tau}$ be a topological space.

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

$x \in H$ is an isolated point of $H$ :
 * $\exists U \in \tau: U \cap H = \set x$

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