Complete lattices

Abbreviation: CLat

Definition

A complete lattice is a structure L = (L,∨,∧) such that ∨,∧ map subsets of L to elements of L and
(L,∨,∧) is a lattice, where x∨y = ∨{x,y} and x∧y = ∧{x,y},
∨S is the least upper bound of S, and
∧S is the greatest lower bound of S with respect to the lattice order.

Morphisms

Let L and M be complete lattices. A morphism from L to M is a function h : L→M that is a complete homomorphism: h(∨S) = ∨h[S] and h(∧S) = ∧h[S].

Some results

Examples

(P(X),∪,∩), the set of all subsets of a set X, with union and intersection of families of sets.

Properties

Subclasses

Superclasses