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 (Order Theory), where an filter is defined in the more general context of Order Theory


 * Meet Semilattice Filter iff Ordered Set Filter, where it is shown that in a meet semilattice the definition of (meet semilattice) filter is equivalent to the definition of (ordered set) filter.


 * Definition:Filter (Lattice), where a filter is defined in the context of a lattice


 * Equivalence of Definitions of Lattice Filter, where it is shown that in a lattice the definition of (lattice) filter is equivalent to the definition of (meet semilattice) filter.


 * Definition:Ideal (Join Semilattice), where the concept of ideal, the dual concept of a filter, is defined.