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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 (''cpo''s), which constitute a strictly more general class of partially ordered sets. More specific complete lattices are complete Boolean algebras and complete Heyting algebras (''locales''). == Formal definition == A partially ordered set (''L'', ≤) is a ''complete lattice'' if every subset ''A'' of ''L'' has both a greatest lower bound (the infimum, also called the ''meet'') and a least upper bound (the supremum, also called the ''join'') in (''L'', ≤). The ''meet'' is denoted by , and the ''join'' by . Note that in the special case where ''A'' is the empty set, the meet of ''A'' will be the greatest element of ''L''. Likewise, the join of the empty set yields the least element. Since the definition also assures the existence of binary meets and joins, complete lattices thus form a special class of bounded lattices. More implications of the above definition are discussed in the article on completeness properties in order theory. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Complete lattice」の詳細全文を読む スポンサード リンク
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