Definition:Lattice Filter/Definition 2

Definition
Let $\struct {S, \vee, \wedge, \preccurlyeq}$ be a lattice.

Let $F \subseteq S$ be a non-empty subset of $S$.

$F$ is a (lattice) filter of $S$ $F$ is a meet semilattice filter

Also see

 * Equivalence of Definitions of Lattice Filter