Definition 5.2.6 (Filter Subbase).label Let $X$ be a set and $\fB_{0} \subset 2^{X}$ be a non-empty collection, then $\fB_{0}$ is a filter subbase if for any $\seqf{E_j}\subset \fB_{0}$, $\bigcap_{j = 1}^{n} E_{j} \ne \emptyset$.
Definition 5.2.6 (Filter Subbase).label Let $X$ be a set and $\fB_{0} \subset 2^{X}$ be a non-empty collection, then $\fB_{0}$ is a filter subbase if for any $\seqf{E_j}\subset \fB_{0}$, $\bigcap_{j = 1}^{n} E_{j} \ne \emptyset$.