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 $\mathcal F$.