# Definition:Limit Point/Topology/Set/Definition 5

< Definition:Limit Point | Topology | Set

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## 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 there is a sequence $\left\langle{x_n}\right\rangle$ in $A$ such that $x$ is a limit point of $\left\langle{x_n}\right\rangle$, considered as sequence in $S$.