Definition 4.2.1 (Filter). Let $X$ be a set, a filter $\fF \subset 2^{X}$ is a non-empty family of sets such that:
For any $E \in \fF$ and $X \supset F \supset E$, $F \in \fF$.
For any $E, F \in \fF$, $E \cap F \in \fF$.
$\emptyset \not\in \fF$
Definition 4.2.1 (Filter). Let $X$ be a set, a filter $\fF \subset 2^{X}$ is a non-empty family of sets such that:
For any $E \in \fF$ and $X \supset F \supset E$, $F \in \fF$.
For any $E, F \in \fF$, $E \cap F \in \fF$.
$\emptyset \not\in \fF$