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:
“Man finds nothing so intolerable as to be in a state of complete rest, without passions, without occupation, without diversion, without effort. Then he feels his nullity, loneliness, inadequacy, dependence, helplessness, emptiness.”
—Blaise Pascal (1623–1662)