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- Limit-preserving_function_(order_theory) 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.".
- Limit-preserving_function_(order_theory) wikiPageID "520517".
- Limit-preserving_function_(order_theory) wikiPageLength "8479".
- Limit-preserving_function_(order_theory) wikiPageOutDegree "30".
- Limit-preserving_function_(order_theory) wikiPageRevisionID "592721602".
- Limit-preserving_function_(order_theory) wikiPageWikiLink Adjoint_functor_theorem_(order_theory).
- Limit-preserving_function_(order_theory) wikiPageWikiLink Category:Order_theory.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Category_theory.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Complete_Heyting_algebra.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Completeness_(order_theory).
- Limit-preserving_function_(order_theory) wikiPageWikiLink Directed_set.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Distributive_lattice.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Domain_theory.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Duality_(order_theory).
- Limit-preserving_function_(order_theory) wikiPageWikiLink Function_(mathematics).
- Limit-preserving_function_(order_theory) wikiPageWikiLink Functor.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Galois_connection.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Homomorphism.
- Limit-preserving_function_(order_theory) wikiPageWikiLink If_and_only_if.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Infimum_and_supremum.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Lattice_(order).
- Limit-preserving_function_(order_theory) wikiPageWikiLink Limit_(category_theory).
- Limit-preserving_function_(order_theory) wikiPageWikiLink Mathematical_analysis.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Mathematics.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Monotonic_function.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Order_theory.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Partially_ordered_set.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Pointless_topology.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Scott_continuity.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Topology.
- Limit-preserving_function_(order_theory) wikiPageWikiLink Universal_algebra.
- Limit-preserving_function_(order_theory) wikiPageWikiLinkText "Limit-preserving function (order theory)".
- Limit-preserving_function_(order_theory) wikiPageWikiLinkText "Limit-preserving function".
- Limit-preserving_function_(order_theory) wikiPageWikiLinkText "Limit-preserving_function_(order_theory)".
- Limit-preserving_function_(order_theory) wikiPageWikiLinkText "Preserving".
- Limit-preserving_function_(order_theory) wikiPageWikiLinkText "limit-preserving functions".
- Limit-preserving_function_(order_theory) wikiPageWikiLinkText "limit-preserving_function_(order_theory)".
- Limit-preserving_function_(order_theory) wikiPageWikiLinkText "preserve".
- Limit-preserving_function_(order_theory) wikiPageWikiLinkText "preserves".
- Limit-preserving_function_(order_theory) wikiPageUsesTemplate Template:Unreferenced.
- Limit-preserving_function_(order_theory) subject Category:Order_theory.
- Limit-preserving_function_(order_theory) type Field.
- Limit-preserving_function_(order_theory) comment "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.".
- Limit-preserving_function_(order_theory) label "Limit-preserving function (order theory)".
- Limit-preserving_function_(order_theory) sameAs Q269441.
- Limit-preserving_function_(order_theory) sameAs m.02k_l0.
- Limit-preserving_function_(order_theory) sameAs Q269441.
- Limit-preserving_function_(order_theory) sameAs 极限保持函数.
- Limit-preserving_function_(order_theory) wasDerivedFrom Limit-preserving_function_(order_theory)?oldid=592721602.
- Limit-preserving_function_(order_theory) isPrimaryTopicOf Limit-preserving_function_(order_theory).