Definition:Limit Point/Topology/Set/Definition 5
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Definition
Let $T = \left({S, \tau}\right)$ be a topological space.
Let $A \subseteq S$.
this definition is not equivalent to the others
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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 $S$.