\begin{definition}[Definition:Cluster Point of Filter]
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 $\FF$'''.
\end{definition}