A filter base $\mathcal{B}$ is a family of non-empty subsets of a Set $X$ such that if $A, B \in \mathcal{B}$ then there exists $C \in \mathcal{B}$ such that $C \subset A \cap B$.

This can be used to construct a Filter on a set:

This notion can also be extended so that a family of sets forming the filter base generates the filters forming the Neighbourhood structure of a Neighbourhood space, or of a Topological space. In this case we call a base, or a Basis of a topology . For a topological space, the arbitrary unions of set in the filter base can be considered to generate the open sets

A filter base can in turn be generated by a Filter subbase