Definition:Cluster Point of Filter

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 $\FF$.