Definition:Cluster Point of Filter

Definition

Let $X$ be a set, and $\mathcal P \left({X}\right)$ be the power set of $X$.

Let $\mathcal F \subset \mathcal P \left({X}\right)$ be a filter on $X$.

Let $x \in X$ be an element of every set in $\mathcal F$:

$x \in X: \forall U \in \mathcal F: x \in U$

Then $x$ is a cluster point of $\mathcal F$.

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 1$: Filters