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:
“Short of a wholesale reform of college athletics—a complete breakdown of the whole system that is now focused on money and power—the women’s programs are just as doomed as the men’s are to move further and further away from the academic mission of their colleges.... We have to decide if that’s the kind of success for women’s sports that we want.”
—Christine H. B. Grant, U.S. university athletic director. As quoted in the Chronicle of Higher Education, p. A42 (May 12, 1993)