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On topological properties of Fréchet locally convex spaces

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On topological properties of Fréchet locally convex spaces

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dc.contributor.author Gabriyelyan, S.S es_ES
dc.contributor.author Kakol, Jerzy Marian es_ES
dc.contributor.author Kubzdela, Albert es_ES
dc.contributor.author López Pellicer, Manuel es_ES
dc.date.accessioned 2016-12-21T14:10:27Z
dc.date.available 2016-12-21T14:10:27Z
dc.date.issued 2015-09-01
dc.identifier.issn 0166-8641
dc.identifier.uri http://hdl.handle.net/10251/75565
dc.description.abstract [EN] We describe the topology of any cosmic space and any N-o-space in terms of special bases defined by partially ordered sets. Using this description we show that a Baire cosmic group is metrizable. Next, we study those locally convex spaces (lcs) E which under the weak topology sigma(E, E') are N-o-spaces. For a metrizable and complete lcs E not containing (an isomorphic copy of) l(1) and satisfying the Heinrich density condition we prove that (E, sigma(E,E')) is an N-o-space if and only if the strong dual of E is separable. In particular, if a Banach space E does not contain l(1), then (E, sigma(E, E')) is an N-o-space if and only if E' is separable. The last part of the paper studies the question: Which spaces (E, sigma(E, E')) are N-o-spaces? We extend, among the others, Michael's results by showing: If E is a metrizable lcs or a (DF)-space whose strong dual E' is separable, then (E, sigma(E, E')) is an N-o-space. Supplementing an old result of Corson we show that, for a Cech-complete Lindelof space X the following are equivalent: (a) X is Polish, (b) C-c(X) is cosmic in the weak topology, (c) the weak*-dual of C-c(X) is an N-o-space. es_ES
dc.description.sponsorship The second and fourth named authors were supported by Generalitat Valenciana, Conselleria d'Educacio, Cultura i Esport, Spain, Grant PROMETEO/2013/058. en_EN
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Topology and its Applications es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject 0-space k-network es_ES
dc.subject Weak topology es_ES
dc.subject Locally convex Fréchet space es_ES
dc.subject 0-space k-network Banach space es_ES
dc.subject Banach space es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title On topological properties of Fréchet locally convex spaces es_ES
dc.type Artículo es_ES
dc.type Comunicación en congreso es_ES
dc.identifier.doi 10.1016/j.topol.2015.05.075
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. Escuela Técnica Superior de Ingeniería Agronómica y del Medio Natural - Escola Tècnica Superior d'Enginyeria Agronòmica i del Medi Natural es_ES
dc.description.bibliographicCitation Gabriyelyan, S.; Kakol, JM.; Kubzdela, A.; López Pellicer, M. (2015). On topological properties of Fréchet locally convex spaces. Topology and its Applications. 192(1):123-137. https://doi.org/10.1016/j.topol.2015.05.075 es_ES
dc.description.accrualMethod S es_ES
dc.relation.conferencename Brazilian Conference on General Topology and Set Theory (STW-2013) es_ES
dc.relation.conferencedate AUG 12-16, 2013 es_ES
dc.relation.conferenceplace Sao Sebastiao, BRAZIL es_ES
dc.relation.publisherversion https://dx.doi.org/10.1016/j.topol.2015.05.075 es_ES
dc.description.upvformatpinicio 123 es_ES
dc.description.upvformatpfin 137 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 192 es_ES
dc.description.issue 1 es_ES
dc.relation.senia 295086 es_ES
dc.identifier.eissn 1879-3207
dc.contributor.funder Generalitat Valenciana es_ES


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