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On weakly compact sets in C(X)

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On weakly compact sets in C(X)

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dc.contributor.author Ferrando, J. C. es_ES
dc.contributor.author López Alfonso, Salvador es_ES
dc.date.accessioned 2021-11-05T14:10:20Z
dc.date.available 2021-11-05T14:10:20Z
dc.date.issued 2021-01-04 es_ES
dc.identifier.issn 1578-7303 es_ES
dc.identifier.uri http://hdl.handle.net/10251/176410
dc.description.abstract [EN] A subset A of a locally convex space E is called (relatively) sequentially complete if every Cauchy sequence {x(n)}(n=1)(infinity) in E contained in A converges to a point x is an element of A (a point x is an element of E). Asanov and Velichko proved that if X is countably compact, every functionally bounded set in C-p (X) is relatively compact, and Baturov showed that if X is a Lindelof Sigma-space, each countably compact (so functionally bounded) set in C-p (X) is a monolithic compact. We show that if X is a Lindelof Sigma-space, every functionally bounded (relatively) sequentially complete set in C-p (X) or in C-w (X), i. e., in C-k (X) equipped with the weak topology, is (relatively) Gul'ko compact. We get some consequences. es_ES
dc.description.sponsorship This work was supported for the first named author by the Grant PGC2018-094431-B-I00 of Ministry of Science, Innovation and Universities of Spain. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Lindelof Sigma-space es_ES
dc.subject Realcompact space es_ES
dc.subject Mu-Space es_ES
dc.subject Sequentially complete set es_ES
dc.subject.classification CONSTRUCCIONES ARQUITECTONICAS es_ES
dc.title On weakly compact sets in C(X) es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s13398-020-00987-0 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-094431-B-I00/ES/ESPACIOS DE FUNCIONES: FUNCIONES ANALITICAS Y OPERADORES DE COMPOSICION. RENORMAMIENTOS Y TOPOLOGIA DESCRIPTIVA/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Construcciones Arquitectónicas - Departament de Construccions Arquitectòniques es_ES
dc.description.bibliographicCitation Ferrando, JC.; López Alfonso, S. (2021). On weakly compact sets in C(X). Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 115(2):1-8. https://doi.org/10.1007/s13398-020-00987-0 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s13398-020-00987-0 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 8 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 115 es_ES
dc.description.issue 2 es_ES
dc.relation.pasarela S\424990 es_ES
dc.contributor.funder MINISTERIO DE CIENCIA, INNOVACIÓN y UNIVERSIDADES es_ES
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