# Definition:Accumulation Point/Set

< Definition:Accumulation Point(Redirected from Definition:Accumulation Point of Set)

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## Definition

Let $\struct {S, \tau}$ be a topological space.

Let $A \subseteq S$.

Let $x \in S$.

Then $x$ is an **accumulation point** of $A$ if and only if:

- $x \in \map \cl {A \setminus \set x}$

where $\cl$ denotes the (topological) closure of a set.

## Also known as

An **accumulation point** is also known as a **cluster point**.

Some sources refer to an **accumulation point** as a limit point, but $\mathsf{Pr} \infty \mathsf{fWiki}$ prefers to maintain a distinction between the two concepts.

## Also see

- Results about
**accumulation points**can be found**here**.

## Sources

- Mizar article TOPGEN_1:def 2