Definition:Filter Sub-Basis

Definition
Let $S$ be a set.

Let $\powerset S$ denote the power set of $S$.

Let $\BB \subset \powerset S$ be a set of subsets of $\powerset S$ which satisfies the finite intersection property.

That is, the intersection of any finite number of sets in $\BB$ is not empty.

Then $\BB$, together with the finite intersections of all its elements, is a basis for a filter $\FF$ on $S$.

Thus $\BB$ is a sub-basis for $\FF$.

Also see

 * Definition:Basis (Topology)


 * Definition:Sub-Basis


 * Definition:Filter Basis