# complete lattice

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complete lattice
A partially ordered set in which all subsets have both a supremum (join) and an infimum (meet).

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• Complete lattice — 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… …   Wikipedia

• Lattice (order) — See also: Lattice (group) The name lattice is suggested by the form of the Hasse diagram depicting it. Shown here is the lattice of partitions of a four element set {1,2,3,4}, ordered by the relation is a refinement of . In mathematics, a… …   Wikipedia

• Complete Heyting algebra — In mathematics, especially in order theory, a complete Heyting algebra is a Heyting algebra which is complete as a lattice. Complete Heyting algebras are the objects of three different categories; the category CHey, the category Loc of locales,… …   Wikipedia

• Complete Boolean algebra — This article is about a type of mathematical structure. For complete sets of Boolean operators, see Functional completeness. In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound) …   Wikipedia

• Complete category — In mathematics, a complete category is a category in which all small limits exist. That is, a category C is complete if every diagram F : J → C where J is small has a limit in C. Dually, a cocomplete category is one in which all small… …   Wikipedia

• Complete partial order — In mathematics, directed complete partial orders and ω complete partial orders (abbreviated to dcpo, ωcpo or sometimes just cpo) are special classes of partially ordered sets, characterized by particular completeness properties. Complete partial… …   Wikipedia

• Lattice problem — In computer science, lattice problems are a class of optimization problems on lattices. The conjectured intractability of such problems is central to construction of secure lattice based cryptosystems. For applications in such cryptosystems,… …   Wikipedia

• Lattice reduction — In mathematics, the goal of lattice basis reduction is given an integer lattice basis as input, to find a basis with short, nearly orthogonal vectors. This is realized using different algorithms, whose running time is usually at least exponential …   Wikipedia

• complete — completable, adj. completedness, n. completely, adv. completeness, n. completer, n. completive, adj. completively, adv. /keuhm pleet /, adj., v., completed, completing. adj …   Universalium

• Completely distributive lattice — In the mathematical area of order theory, a completely distributive lattice is a complete lattice in which arbitrary joins distribute over arbitrary meets. Formally, a complete lattice L is said to be completely distributive if, for any doubly… …   Wikipedia