Definition:Isolated Point (Topology)/Space

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

$x \in S$ is an isolated point of $T$ iff:
 * $\exists U \in \tau: U = \left\{{x}\right\}$

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