Definition:Superfilter

Let $$X$$ be a topological space and $$\mathcal{F}, \mathcal{F}' \subset \mathcal{P}(X)$$ two filters on $$X$$. Then $$\mathcal{F}'$$ is called a superfilter of $$\mathcal{F}$$ if $$\mathcal{F} \subseteq \mathcal{F}'$$.