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 $$\mathcal F$$.