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Completeness (in topology)

concept 1 articles 13 citations 15 shown relations

MathematicsTopology

A property of a space requiring that sequences, directions or families of sets, satisfying the

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2020 Mathematics Subject Classification: Primary: 54-XX [MSN][ZBL]

A property of a space requiring that sequences, directions or families of sets, satisfying the Cauchy condition (or appropriate generalizations of it, see Cauchy filter) converge. (See also Complete metric space, Complete uniform space, Complete space, Completion, and Cauchy criteria.)

How to Cite This Entry:
Completeness (in topology). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Completeness_(in_topology)&oldid=36902

This article was adapted from an original article by A.V. Arkhangel'skii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article

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TopologyMathematics / Topologymethod: keyword_rule - confidence: 0.68suggested

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Completeness (in topology)encyclopedia_of_mathematics

Citations

Completionoutgoing citation Complete spaceoutgoing citation Cauchy criteriaoutgoing citation Complete uniform spaceoutgoing citation Complete metric spaceoutgoing citation Cauchy filteroutgoing citation Cauchy sequenceoutgoing citation Cauchy criteriaincoming citation Ekeland variational principleincoming citation Topology, generalincoming citation Banach spaceincoming citation Topological structuresincoming citation Compactificationincoming citation

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discussesarticle:eom--completeness-in-topology--53dec2ab1f -> concept:completeness-in-topologyconfidence: 1.00 - provenance: encyclopedia_of_mathematicsconfirmed

citesconcept:completeness-in-topology -> concept:completionconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:completeness-in-topology -> concept:complete-spaceconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:completeness-in-topology -> concept:cauchy-criteriaconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:completeness-in-topology -> concept:complete-uniform-spaceconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:completeness-in-topology -> concept:complete-metric-spaceconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:completeness-in-topology -> concept:cauchy-filterconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:completeness-in-topology -> concept:cauchy-sequenceconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:cauchy-criteria -> concept:completeness-in-topologyconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:ekeland-variational-principle -> concept:completeness-in-topologyconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:topology-general -> concept:completeness-in-topologyconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:banach-space -> concept:completeness-in-topologyconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:topological-structures -> concept:completeness-in-topologyconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:compactification -> concept:completeness-in-topologyconfidence: 1.00 - provenance: article backlink extractionreviewed

subcategory_ofconcept:completeness-in-topology -> topic:topologyconfidence: 0.68 - provenance: keyword_rule classificationsuggested

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