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

 * User:Leigh.Samphier/OrderTheory/Definition:Filter (Order Theory)


 * User:Leigh.Samphier/OrderTheory/Definition:Filter (Lattice)


 * User:Leigh.Samphier/OrderTheory/Meet Semilattice Filter iff Ordered Set Filter