Definition:Lattice Filter

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

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

Also known as
In some sources a lattice filter is called a dual ideal.

Also see

 * Equivalence of Definitions of Lattice Filter


 * Definition:Meet Semilattice Filter
 * Definition:Filter
 * Meet Semilattice Filter iff Ordered Set Filter
 * Definition:Lattice Ideal