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