Definition:Limit Point/Topology/Set/Definition 4

Definition

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

Let $A \subseteq S$.

A point $x \in S$ is a limit point of $A$ if and only if $\left({S \setminus A}\right) \cup \left\{{x}\right\}$ is not a neighborhood of $x$.