Definition:Filter Basis/Definition 2

Definition
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 $\FF$ :
 * $\forall U \in \FF: \exists V \in \BB: V \subseteq U$

Also known as
A filter basis is also known as a filter base.

Also see

 * Equivalence of Definitions of Filter Basis