Definition:Cluster Point of Filter

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Definition

Let $S$ be a set.

Let $\powerset S$ denote the power set of $S$.

Let $\FF \subset \powerset X$ be a filter on $S$.


Let $x \in S$ be an element of every set in $\FF$:

$x \in X: \forall U \in \FF: x \in U$

Then $x$ is a cluster point of $\FF$.


Sources