Definition:Meet Semilattice Filter

Definition
Let $\struct {S, \wedge, \preccurlyeq}$ be a meet semilattice.

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

Then $F$ is a meet semilattice ideal of $S$ $F$ satisifies the meet semilattice filter axioms:

Also see

 * Definition:Filter
 * Meet Semilattice Filter iff Ordered Set Filter
 * Definition:Lattice
 * Equivalence of Definitions of Lattice Filter
 * Definition:Join Semilattice Ideal