In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). Complete lattices appear in many applications in mathematics and computer science. Being a special instance of lattices, they are studied both in order theory and universal algebra.
Complete lattices must not be confused with complete partial orders (cpos), which constitute a strictly more general class of partially ordered sets. More specific complete lattices are complete Boolean algebras and complete Heyting algebras (locales).
Read more about Complete Lattice: Formal Definition, Examples, Morphisms of Complete Lattices, Representation, Further Results
Famous quotes containing the word complete:
“In the course of the actual attainment of selfish ends—an attainment conditioned in this way by universality—there is formed a system of complete interdependence, wherein the livelihood, happiness, and legal status of one man is interwoven with the livelihood, happiness, and rights of all. On this system, individual happiness, etc. depend, and only in this connected system are they actualized and secured.”
—Georg Wilhelm Friedrich Hegel (1770–1831)