Compact covers and function spaces

Kakol, J.; López Pellicer, Manuel; Okunev, O.

doi:10.1016/j.jmaa.2013.09.046

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Compact covers and function spaces

dc.contributor.author	Kakol, J.	es_ES
dc.contributor.author	López Pellicer, Manuel	es_ES
dc.contributor.author	Okunev, O.	es_ES
dc.date.accessioned	2015-11-02T12:49:50Z
dc.date.available	2015-11-02T12:49:50Z
dc.date.issued	2014-03-01
dc.identifier.issn	0022-247X
dc.identifier.uri	http://hdl.handle.net/10251/56861
dc.description.abstract	For a Tychonoff space X, we denote by Cp(X) and Cc(X) the space of continuous real-valued functions on X equipped with the topology of pointwise convergence and the compact-open topology respectively. Providing a characterization of the Lindelof $Sigma$-property of X in terms of Cp(X), we extend Okunev's results by showing that if there exists a surjection from Cp(X) onto Cp(Y) (resp. from Lp(X) onto Lp(Y)) that takes bounded sequences to bounded sequences, then $nu$Y is a Lindelof $Sigma$-space (respectively K-analytic) if $nu$X has this property. In the second part, applying Christensen's theorem, we extend Pelant's result by proving that if X is a separable completely metrizable space and Y is first countable, and there is a quotient linear map from Cc(X) onto Cc(Y), then Y is a separable completely metrizable space.We study also a non-separable case, and consider a different approach to the result of J. Baars, J. de Groot, J. Pelant and V. Valov, which is based on the combination of two facts: Complete metrizability is preserved by lp-equivalence in the class of metric spaces (J. Baars, J. de Groot, J. Pelant). If X is completely metrizable and lp-equivalent to a first-countable Y, then Y is metrizable (V. Valov). Some additional results are presented.	es_ES
dc.description.sponsorship	The research was supported for the first named author by National Center of Science, Poland, Grant No. N N201 605340, and for the first and second named authors by Generalitat Valenciana, Conselleria d'Educacio i Esport, Spain, Grant PROMETEO/2013/058.	en_EN
dc.language	Inglés	es_ES
dc.publisher	Elsevier	es_ES
dc.relation.ispartof	Journal of Mathematical Analysis and Applications	es_ES
dc.rights	Reserva de todos los derechos	es_ES
dc.subject	Compact resolution	es_ES
dc.subject	C(X) and Lp(X) spaces	es_ES
dc.subject	Cech-complete space	es_ES
dc.subject	Lindelöf $Sigma$, K-analytic, analytic spaces	es_ES
dc.subject	Lp,lc and t-equivalence	es_ES
dc.subject	Point wise countable type spaces	es_ES
dc.subject	Polish space	es_ES
dc.subject	Realcompactification	es_ES
dc.subject	$mu$-space	es_ES
dc.subject	Web-bounded spaces.	es_ES
dc.subject.classification	MATEMATICA APLICADA	es_ES
dc.title	Compact covers and function spaces	es_ES
dc.type	Artículo	es_ES
dc.identifier.doi	10.1016/j.jmaa.2013.09.046
dc.relation.projectID	info:eu-repo/grantAgreement/NCN//N N201 605340/	es_ES
dc.relation.projectID	info:eu-repo/grantAgreement/GVA//PROMETEO%2F2013%2F058/	es_ES
dc.rights.accessRights	Abierto	es_ES
dc.contributor.affiliation	Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada	es_ES
dc.description.bibliographicCitation	Kakol, J.; López Pellicer, M.; Okunev, O. (2014). Compact covers and function spaces. Journal of Mathematical Analysis and Applications. 411(1):372-380. https://doi.org/10.1016/j.jmaa.2013.09.046	es_ES
dc.description.accrualMethod	S	es_ES
dc.relation.publisherversion	http://dx.doi.org/10.1016/j.jmaa.2013.09.046	es_ES
dc.description.upvformatpinicio	372	es_ES
dc.description.upvformatpfin	380	es_ES
dc.type.version	info:eu-repo/semantics/publishedVersion	es_ES
dc.description.volume	411	es_ES
dc.description.issue	1	es_ES
dc.relation.senia	251443	es_ES
dc.contributor.funder	Generalitat Valenciana	es_ES
dc.contributor.funder	National Science Centre, Polonia	es_ES