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 $S$ if and only if $F$ is a meet semilattice filter.

Also see

• Equivalence of Definitions of Lattice Filter

Sources

• 1982: Peter T. Johnstone: Stone Spaces: Chapter $\text {I}$: Preliminaries, Definition $2.2$