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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 (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).

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  • Complete lattice
  • Retículo completo
  • 完備束
  • Полная решётка
  • 完全格
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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 (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).
  • En matemáticas y ciencias de la computación, un retículo completo es un conjunto parcialmente ordenado en que todos los subconjuntos tienen un supremo (join) y un ínfimo (meet). Siendo una instancia especial de retículos, son estudiados en teoría del orden y álgebra universal. Los retículos completos no deben ser confundidos con órdenes parciales completos, los cuales constituyen una clase estrictamente más general de conjuntos parcialmente ordenados. Retículos completos más específicos constituyen álgebras booleanas completas y álgebras de Heyting completas.
  • 数学の一分野順序論における完備束(英: complete lattice)とは部分集合が常に上限と下限を持つ半順序集合のことである。完備束は束の重要な例で順序集合論及び普遍代数の研究対象であり、数学及び計算機科学に多くの応用を持つ。 順序集合上の完備性には様々な異なる定義があるので注意を要する(例えば完備半順序 (CPO) は完備束とは異なる概念である)。特に重要な完備束のクラスとして完備ブール代数や完備ハイティング代数 (locale) がある。
  • Полная решётка — частично упорядоченное множество, в котором всякое непустое подмножество имеет точную верхнюю и нижнюю грань, называемые обычно объединением и пересечением элементов подмножества и обозначаемые и (или просто и ) соответственно. Относительно операций объединения и пересечения полная решётка является решёткой.
  • 在数学中,完全格是在其中所有子集都有上确界(并)和下确界(交)的偏序集。完全格出现于数学和计算机科学的很多应用中。作为格的特殊实例,在序理论和泛代数中都有所研究。 完全格一定不能混淆于完全偏序(cpo),它构成严格的更加一般的一个偏序集合类别。更特殊的完全格是完全布尔代数和完全Heyting代数(locale)。
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