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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). A lattice which satisfies at least one of these properties is known as a conditionally complete lattice. Specifically, every non-empty finite lattice is complete. 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.

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rdf:type	yago:WikicatClosureOperators yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Operator113786413 yago:Relation100031921
rdfs:label	Úplný svaz (cs) Ολοκληρωμένο πλέγμα (el) Retículo completo (es) Complete lattice (en) Kekisi lengkap (in) 완비 격자 (ko) 完備束 (ja) 完全格 (zh)
rdfs:comment	Úplný svaz je matematický pojem z oboru teorie uspořádání, který vymezuje mezi uspořádanými množinami ty, které jsou uspořádány „rozumně“ (to znamená, že zachovávají suprema a infima). Na rozdíl od svazu, kde je zachování suprem a infim požadováno pro dvouprvkové podmnožiny, pro úplný svaz je toto požadováno pro libovolné (tedy i nekonečné) podmnožiny. (cs) 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 y . (es) Dalam matematika, kisi lengkap adalah himpunan yang tersusun sebagian di mana semua himpunan bagian memiliki supremum (gabung) dan infimum (pertemuan). Kisi lengkap pada aplikasi dalam matematika dan ilmu komputer. Sebagai contoh khusus dari kisi, dengan teori urutan dan aljabar universal. Kisi kompleks tidak disamakan dengan ( CPO ), yang merupakan kelas umum dari urutan himpunan sebagian. Kisi kompleks spesifik adalah dan ( lokal ). (in) 순서론에서 완비 격자(完備格子, 영어: complete lattice)는 임의의 크기의 이음 및 만남이 존재하는 격자이다. (ko) 数学の一分野における完備束（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。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や (locale) がある。 (ja) 完全格又稱完備格，（英語：complete lattice），在数学中是代表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海廷代数（locale）。 (zh) Στα μαθηματικά, ένα ολοκληρωμένο (ή πλήρες) πλέγμα είναι ένα μερικώς διατεταγμένο σύνολο (partially ordered set) στο οποίο όλα τα υποσύνολα έχουν ένα supremum sup (που ονομάζεται και join ή ένωση και είναι το ελάχιστο άνω φράγμα) και ένα infimum inf (που ονομάζεται και meet ή τομή και είναι το μέγιστο κάτω φράγμα).Τα ολοκληρωμένα πλέγματα χρησιμοποιούνται σε πολλές εφαρμογές στα μαθηματικά και στην επιστήμη των υπολογιστών. Επειδή τα ολοκληρωμένα πλέγματα αποτελούν μία ειδική περίπτωση πλεγμάτων, μελετώνται επίσης στη θεωρία διατάξεων και στην καθολική άλγεβρα. (el) In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). A lattice which satisfies at least one of these properties is known as a conditionally complete lattice. Specifically, every non-empty finite lattice is complete. 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. (en)
dcterms:subject	Lattice theory Closure operators
Wikipage page ID	44777 (xsd:integer)
Wikipage revision ID	1109271711 (xsd:integer)
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