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
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Filters