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- Directed_set abstract "In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set A together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that every pair of elements has an upper bound: In other words, for any a and b in A there must exist a c in A with a ≤ c and b ≤ c.Directed sets are a generalization of nonempty totally ordered sets, that is, all totally ordered sets are directed sets (contrast partially ordered sets which need not be directed). In topology, directed sets are used to define nets, which generalize sequences and unite the various notions of limit used in analysis. Directed sets also give rise to direct limits in abstract algebra and (more generally) category theory.".
- Directed_set thumbnail Directed_set,_but_no_join_semi-lattice.gif?width=300.
- Directed_set wikiPageID "9165".
- Directed_set wikiPageRevisionID "573973943".
- Directed_set hasPhotoCollection Directed_set.
- Directed_set subject Category:General_topology.
- Directed_set subject Category:Mathematical_relations.
- Directed_set subject Category:Order_theory.
- Directed_set comment "In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set A together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that every pair of elements has an upper bound: In other words, for any a and b in A there must exist a c in A with a ≤ c and b ≤ c.Directed sets are a generalization of nonempty totally ordered sets, that is, all totally ordered sets are directed sets (contrast partially ordered sets which need not be directed). ".
- Directed_set label "Conjunto direcionado".
- Directed_set label "Directed set".
- Directed_set label "Ensemble ordonné filtrant".
- Directed_set label "Gerichtete Menge".
- Directed_set label "Insieme diretto".
- Directed_set label "Zbiór skierowany".
- Directed_set label "Направленное множество".
- Directed_set label "有向集合".
- Directed_set label "有向集合".
- Directed_set sameAs Gerichtete_Menge.
- Directed_set sameAs Ensemble_ordonné_filtrant.
- Directed_set sameAs Insieme_diretto.
- Directed_set sameAs 有向集合.
- Directed_set sameAs Zbiór_skierowany.
- Directed_set sameAs Conjunto_direcionado.
- Directed_set sameAs m.02j4r.
- Directed_set sameAs Q1513048.
- Directed_set sameAs Q1513048.
- Directed_set wasDerivedFrom Directed_set?oldid=573973943.
- Directed_set depiction Directed_set,_but_no_join_semi-lattice.gif.
- Directed_set isPrimaryTopicOf Directed_set.
