Accumulation Point

An accumulation point of a subset $S\subseteq X$ of a Topological Space $X$ is a point $x:X$ that can be approximated by points of $S$ that are distinct from $x$.

Explicitly, $x$ is an accumulation point of $S$ if for every Open Neighborhood $x\in U\in\mathcal{O}({X})$, the intersection $U\cap S$ contains a point $y\neq x$.