Limit Point

Definition

Consider a subset $A$ of a Topological Space $(X,\mathcal{T})$. A point $x\in X$ is a limit point of $A$ if every Neighborhood of $x$ contains a point of $A$ different from $x$ itself. $x\in X\text{s.t.}\forall {\mathcal{N}}_x,{\mathcal{N}}_x\cap (A-\{x\})\ne \varnothing$

And the set of all limit points of $A$ is notated as $A^{\prime }$ $A^{\prime }=\{x\in X|\forall {\mathcal{N}}_x,{\mathcal{N}}_x\cap (A-\{x\})\ne \varnothing \}$