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Topological groups with dense compactly generated subgroups

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Topological groups with dense compactly generated subgroups

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dc.contributor.author Fujita, Hiroshi es_ES
dc.contributor.author Shakhmatov, Dimitri es_ES
dc.date.accessioned 2017-05-30T10:55:27Z
dc.date.available 2017-05-30T10:55:27Z
dc.date.issued 2002-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/82022
dc.description.abstract [EN] A topological group G is: (i) compactly generated if it contains a compact subset algebraically generating G, (ii) -compact if G is a union of countably many compact subsets, (iii) 0-bounded if arbitrary neighborhood U of the identity element of G has countably many translates xU that cover G, and (iv) finitely generated modulo open sets if for every non-empty open subset U of G there exists a finite set F such that F U algebraically generates G. We prove that: (1) a topological group containing a dense compactly generated subgroup is both 0-bounded and finitely generated modulo open sets, (2) an almost metrizable topological group has a dense compactly generated subgroup if and only if it is both 0-bounded and finitely generated modulo open sets, and (3) an almost metrizable topological group is compactly generated if and only if it is -compact and finitely generated modulo open sets. es_ES
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València
dc.relation.ispartof Applied General Topology
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Topological group es_ES
dc.subject Compactly generated group es_ES
dc.subject Dense subgroup es_ES
dc.subject Almost metrizable group es_ES
dc.subject ℵ0-bounded group es_ES
dc.subject Paracompact p-space es_ES
dc.subject Metric space es_ES
dc.subject σ-compact space es_ES
dc.subject Space of countable type es_ES
dc.title Topological groups with dense compactly generated subgroups es_ES
dc.type Artículo es_ES
dc.date.updated 2017-05-30T09:28:36Z
dc.identifier.doi 10.4995/agt.2002.2115
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Fujita, H.; Shakhmatov, D. (2002). Topological groups with dense compactly generated subgroups. Applied General Topology. 3(1):85-89. https://doi.org/10.4995/agt.2002.2115 es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2002.2115 es_ES
dc.description.upvformatpinicio 85 es_ES
dc.description.upvformatpfin 89 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 3
dc.description.issue 1
dc.identifier.eissn 1989-4147
dc.provenance Universitat Politècnica de València
dc.description.references H. Fujita and D. B. Shakhmatov, A characterization of compactly generated metrizable groups, Proc. Amer. Math. Soc., to appear. es_ES
dc.description.references B.A. Pasynkov, Almost-metrizable topological groups (in Russian), Dokl. Akad. Nauk SSSR 161 (1965), 281-284. es_ES


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