Definition:Limit Point/Topology/Set/Definition 3

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 $A$ $x$ is an adherent point of $A$ but is not an isolated point of $A$.

Also see

 * Equivalence of Definitions of Limit Point, which proves that this definition is equivalent to the Definition from Closure