Real Analysis/Limit Points (Accumulation Points)

Definition

Let (X,d) be a metric space, and let $A \subset X$. We call $x \in X$ a limit point of A if for any ε > 0 there exists some $y \neq x$ such that $y \in B(x,\epsilon)\cap A$.

We denote the set lim(A) the set of all $x \in X$ such that x is a limit point of A.