Limit Point

Let $(X,d)$ be a metric space.
Given $A\subseteq X$.
Say $x\in X$ is a limit point of $A$ iff
$B^{\ast }(x,\epsilon )\cap A\ne \varnothing \forall \epsilon >0$
Where $B^{\ast }(x,\epsilon )$ is the punctured open ball of radius $\epsilon$ centered at $x$.