Definition:Filter

Definition
Let $\left({S, \preccurlyeq}\right)$ be an ordered set.

A filter of $\left({S, \preccurlyeq}\right)$ (or a filter on $\left({S, \preccurlyeq}\right)$) is a subset $\mathcal F \subseteq S$ which satisfies the following conditions:

Also see

 * Definition:Filter on Set