Definition:Limit Point/Topology/Set/Definition 1

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 $A$ iff every open neighborhood $U$ of $x$ satisfies:
 * $A \cap \left({U \setminus \left\{{x}\right\}}\right) \ne \varnothing$

That is, iff every open set $U \in \tau$ such that $x \in U$ contains some point of $A$ distinct from $x$.