# Real Analysis/Limit Points (Accumulation Points)

## Definition edit

Let be a metric space, and let . We call a limit point of if for any there exists some such that .

We denote the set the set of all such that is a limit point of .

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 $\epsilon >0$ 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 $A$ .