Accumulation Point

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

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