\begin{definition}[Definition:Filter Basis/Definition 2]
Let $S$ be a set.
Let $\BB$ be a subset of a filter $\FF$ on $S$ such that $\BB \ne \O$.
Then $\BB$ is a '''filter basis''' of $\FF$ {{iff}}:
:$\forall U \in \FF: \exists V \in \BB: V \subseteq U$
\end{definition}