About: Limit-preserving function (order theory)

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In the mathematical area of order theory, one often speaks about functions that preserve certain limits, i.e. certain suprema or infima. Roughly speaking, these functions map the supremum/infimum of a set to the supremum/infimum of the image of the set. Depending on the type of sets for which a function satisfies this property, it may preserve finite, directed, non-empty, or just arbitrary suprema or infima. Each of these requirements appears naturally and frequently in many areas of order theory and there are various important relationships among these concepts and other notions such as monotonicity. If the implication of limit preservation is inverted, such that the existence of limits in the range of a function implies the existence of limits in the domain, then one obtains functions th

Attributes	Values
rdfs:label	Limit-preserving function (order theory) (en) 极限保持函数 (zh)
rdfs:comment	在数学领域序理论中，经常谈论保持特定极限也就是特定上确界或下确界的函数。粗略的说，这些函数把一个集合的上确界／下确界映射到这个集合的像的上确界／下确界。依赖于满足这种性质函数所在集合的类型，它可以保持有限、有向、非空或仅为任意的上确界或下确界。其中的每个要求都自然和经常的出现在序理论的很多领域中，在这些概念和其他概念比如单调函数之间有各种重要的联系。如果极限保持的蕴涵是倒转的，使得在函数的值域中极限的存在性蕴涵在定义域中的极限的存在性，则这种函数是极限反射。由于文献中对这些基本概念的定义不总是一致，本文力图明晰之并给出一般性结果和对要点解说。 (zh) In the mathematical area of order theory, one often speaks about functions that preserve certain limits, i.e. certain suprema or infima. Roughly speaking, these functions map the supremum/infimum of a set to the supremum/infimum of the image of the set. Depending on the type of sets for which a function satisfies this property, it may preserve finite, directed, non-empty, or just arbitrary suprema or infima. Each of these requirements appears naturally and frequently in many areas of order theory and there are various important relationships among these concepts and other notions such as monotonicity. If the implication of limit preservation is inverted, such that the existence of limits in the range of a function implies the existence of limits in the domain, then one obtains functions th (en)
dcterms:subject	Order theory
Wikipage page ID	520517 (xsd:integer)
Wikipage revision ID	936614833 (xsd:integer)
Link from a Wikipage to another Wikipage	Monotonic function Homomorphism Universal algebra Order theory Mathematical analysis Mathematics Order theory Function (mathematics) Galois connection Limit (category theory) Complete Heyting algebra Completeness (order theory) Functor Pointless topology Topology Distributive lattice Domain theory Duality (order theory) Lattice (order) Partially ordered set Directed set Supremum Scott-continuous If and only if Category theory Infimum dbr:Adjoint_functor_theorem_(order_theory)
sameAs	Limit-preserving function (order theory) Limit-preserving function (order theory) Limit-preserving function (order theory) Limit-preserving function (order theory)
dbp:wikiPageUsesTemplate	dbt:Unreferenced
has abstract	In the mathematical area of order theory, one often speaks about functions that preserve certain limits, i.e. certain suprema or infima. Roughly speaking, these functions map the supremum/infimum of a set to the supremum/infimum of the image of the set. Depending on the type of sets for which a function satisfies this property, it may preserve finite, directed, non-empty, or just arbitrary suprema or infima. Each of these requirements appears naturally and frequently in many areas of order theory and there are various important relationships among these concepts and other notions such as monotonicity. If the implication of limit preservation is inverted, such that the existence of limits in the range of a function implies the existence of limits in the domain, then one obtains functions that are limit-reflecting. The purpose of this article is to clarify the definition of these basic concepts, which is necessary since the literature is not always consistent at this point, and to give general results and explanations on these issues. (en) 在数学领域序理论中，经常谈论保持特定极限也就是特定上确界或下确界的函数。粗略的说，这些函数把一个集合的上确界／下确界映射到这个集合的像的上确界／下确界。依赖于满足这种性质函数所在集合的类型，它可以保持有限、有向、非空或仅为任意的上确界或下确界。其中的每个要求都自然和经常的出现在序理论的很多领域中，在这些概念和其他概念比如单调函数之间有各种重要的联系。如果极限保持的蕴涵是倒转的，使得在函数的值域中极限的存在性蕴涵在定义域中的极限的存在性，则这种函数是极限反射。由于文献中对这些基本概念的定义不总是一致，本文力图明晰之并给出一般性结果和对要点解说。 (zh)
prov:wasDerivedFrom	wikipedia-en:Limit-preserving_function_(order_theory)?oldid=936614833&ns=0
page length (characters) of wiki page	8479 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Limit-preserving_function_(order_theory)
is Link from a Wikipage to another Wikipage of	List of order theory topics Order theory Completeness (order theory) Distributive lattice Domain theory Glossary of order theory Heyting algebra Limit preserving (order theory) Limit preserving function Limit preserving function (order theory)
is Wikipage redirect of	Limit preserving (order theory) Limit preserving function Limit preserving function (order theory)
is foaf:primaryTopic of	wikipedia-en:Limit-preserving_function_(order_theory)

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