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- Cofinal_(mathematics) abstract "In mathematics, let A be a set and let ≤ be a binary relation on A. Then a subset B of A is said to be cofinal if it satisfies the following condition:For every a ∈ A, there exists some b ∈ B such that a ≤ b.This definition is most commonly applied when A is a partially ordered set or directed set under the relation ≤.Cofinal subsets are very important in the theory of directed sets and nets, where “cofinal subnet” is the appropriate generalization of “subsequence”. They are also important in order theory, including the theory of cardinal numbers, where the minimum possible cardinality of a cofinal subset of A is referred to as the cofinality of A.A subset B of A is said to be coinitial (or dense in the sense of forcing) if it satisfies the following condition:For every a ∈ A, there exists some b ∈ B such that b ≤ a.This is the order-theoretic dual to the notion of cofinal subset.Note that cofinal and coinitial subsets are both dense in the sense of appropriate (right- or left-) order topology.".
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- Cofinal_(mathematics) wikiPageWikiLink Binary_relation.
- Cofinal_(mathematics) wikiPageWikiLink Cardinal_number.
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- Cofinal_(mathematics) wikiPageWikiLink Cardinality.
- Cofinal_(mathematics) wikiPageWikiLink Category:Order_theory.
- Cofinal_(mathematics) wikiPageWikiLink Cauchy_sequence.
- Cofinal_(mathematics) wikiPageWikiLink Cauchy_sequences.
- Cofinal_(mathematics) wikiPageWikiLink Cofinality.
- Cofinal_(mathematics) wikiPageWikiLink Cofinite.
- Cofinal_(mathematics) wikiPageWikiLink Cofiniteness.
- Cofinal_(mathematics) wikiPageWikiLink Complete_metric_space.
- Cofinal_(mathematics) wikiPageWikiLink Complete_space.
- Cofinal_(mathematics) wikiPageWikiLink Directed_set.
- Cofinal_(mathematics) wikiPageWikiLink Duality_(order_theory).
- Cofinal_(mathematics) wikiPageWikiLink Forcing_(mathematics).
- Cofinal_(mathematics) wikiPageWikiLink Function_(mathematics).
- Cofinal_(mathematics) wikiPageWikiLink Greatest_element.
- Cofinal_(mathematics) wikiPageWikiLink Index_of_a_subgroup.
- Cofinal_(mathematics) wikiPageWikiLink Mathematics.
- Cofinal_(mathematics) wikiPageWikiLink Maximal_element.
- Cofinal_(mathematics) wikiPageWikiLink Natural_number.
- Cofinal_(mathematics) wikiPageWikiLink Net_(mathematics).
- Cofinal_(mathematics) wikiPageWikiLink Normal_subgroup.
- Cofinal_(mathematics) wikiPageWikiLink Order_theory.
- Cofinal_(mathematics) wikiPageWikiLink Order_topology.
- Cofinal_(mathematics) wikiPageWikiLink Partially_ordered_set.
- Cofinal_(mathematics) wikiPageWikiLink Power_set.
- Cofinal_(mathematics) wikiPageWikiLink Range_(mathematics).
- Cofinal_(mathematics) wikiPageWikiLink Reflexive_relation.
- Cofinal_(mathematics) wikiPageWikiLink Subnet_(mathematics).
- Cofinal_(mathematics) wikiPageWikiLink Subsequence.
- Cofinal_(mathematics) wikiPageWikiLink Subset.
- Cofinal_(mathematics) wikiPageWikiLink Total_order.
- Cofinal_(mathematics) wikiPageWikiLink Totally_ordered.
- Cofinal_(mathematics) wikiPageWikiLink Transitive_relation.
- Cofinal_(mathematics) wikiPageWikiLink Upper_set.
- Cofinal_(mathematics) wikiPageWikiLink Well-order.
- Cofinal_(mathematics) wikiPageWikiLink Well-ordered.
- Cofinal_(mathematics) wikiPageWikiLinkText "Cofinal (mathematics)".
- Cofinal_(mathematics) wikiPageWikiLinkText "Cofinal".
- Cofinal_(mathematics) wikiPageWikiLinkText "cofinal".
- Cofinal_(mathematics) wikiPageWikiLinkText "coinitial".
- Cofinal_(mathematics) wikiPageWikiLinkText "dense".
- Cofinal_(mathematics) hasPhotoCollection Cofinal_(mathematics).
- Cofinal_(mathematics) wikiPageUsesTemplate Template:Lang_Algebra.
- Cofinal_(mathematics) wikiPageUsesTemplate Template:Reflist.
- Cofinal_(mathematics) subject Category:Order_theory.
- Cofinal_(mathematics) comment "In mathematics, let A be a set and let ≤ be a binary relation on A. Then a subset B of A is said to be cofinal if it satisfies the following condition:For every a ∈ A, there exists some b ∈ B such that a ≤ b.This definition is most commonly applied when A is a partially ordered set or directed set under the relation ≤.Cofinal subsets are very important in the theory of directed sets and nets, where “cofinal subnet” is the appropriate generalization of “subsequence”.".
- Cofinal_(mathematics) label "Cofinal (mathematics)".
- Cofinal_(mathematics) sameAs Sottoinsieme_Cofinale.
- Cofinal_(mathematics) sameAs m.05j8l9.
- Cofinal_(mathematics) sameAs Q5141045.
- Cofinal_(mathematics) sameAs Q5141045.
- Cofinal_(mathematics) sameAs 共尾.
- Cofinal_(mathematics) wasDerivedFrom Cofinal_(mathematics)?oldid=607162615.
- Cofinal_(mathematics) isPrimaryTopicOf Cofinal_(mathematics).