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
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es_ES |
| dc.contributor.author | López Pellicer, Manuel
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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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