Definition:Accumulation Point/Set

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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.