The structure of the poset of regular topologies on a set

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dc.contributor.authorAlas, Ofelia T.es_ES
dc.contributor.authorWilson, Richard G.es_ES
dc.contributor.funderSecretaría de Educación Pública, México
dc.contributor.funderFundação de Amparo à Pesquisa do Estado de São Paulo
dc.contributor.funderUniversitat Jaume I
dc.contributor.funderFundación Bancaja
dc.date.accessioned2017-09-11T11:56:55Z
dc.date.available2017-09-11T11:56:55Z
dc.date.issued2011-04-01
dc.date.updated2017-09-11T11:50:31Z
dc.description.abstract[EN] We study the subposet E3(X) of the lattice L1(X) of all T1-topologies on a set X, being the collections of all T3 topologies on X, with a view to deciding which elements of this partially ordered set have and which do not have immediate predecessors. We show that each regular topology which is not R-closed does have such a predecessor and as a corollary we obtain a result of Costantini that each non-compact Tychonoff space has an immediate predecessor in E3. We also consider the problem of when an R-closed topology is maximal R-closed.en_EN
dc.description.accrualMethodSWORDes_ES
dc.description.bibliographicCitationAlas, OT.; Wilson, RG. (2011). The structure of the poset of regular topologies on a set. Applied General Topology. 12(1):1-13. https://doi.org/10.4995/agt.2011.1695es_ES
dc.description.issue1
dc.description.referencesO. T. Alas, S. Hern’andez, M. Sanchis, M. G. Tkachenko and R. G. Wilson, Adjacency in the partial orders of Tychonoff, regular and locally compact topologies, Acta Math. Hungar. 112, no. 3 (2006), 2005–2025.es_ES
dc.description.referencesO. T. Alas, M. G. Tkachenko and R. G. Wilson, Which topologies have immediate predecessors in the poset of Hausdorff topologies?, Houston Journal Math., to appear.es_ES
dc.description.referencesAlas, O. T., & Wilson, R. G. (2004). Which topologies can have immediate successors in the lattice of T1-topologies? Applied General Topology, 5(2), 231. doi:10.4995/agt.2004.1972es_ES
dc.description.referencesM. Berri, J. Porter and R. M. Stephenson, A survey of minimal topological spaces, Proc. Kanpur Conference, 1968.es_ES
dc.description.referencesC. Costantini, On some questions about posets of topologies on a fixed set, Topology Proc. 32 (2008), 187–225.es_ES
dc.description.referencesR. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.es_ES
dc.description.referencesL. M. Friedler, M. Girou, D. H. Pettey and J. R. Porter, A survey of R-, U-, and CH-closed spaces, Topology Proc. 17 (1992), 71–96.es_ES
dc.description.referencesHechler, S. H. (1976). Two R-Closed Spaces Revisited. Proceedings of the American Mathematical Society, 56(1), 303. doi:10.2307/2041624es_ES
dc.description.referencesR. E. Larson and W. J. Thron, Covering relations in the lattice of T1-topologies, Trans. Amer. Math. Soc. 168 (1972), 101–111.es_ES
dc.description.referencesJ. Porter and R. G. Woods, Extensions and Absolutes of Topological Spaces, Springer Verlag, New York, 1987.es_ES
dc.description.sponsorshipResearch supported by Programa Integral de Fortalecimiento Institucional (PIFI), grant no. 34536-55 (México) and Fundaçãao de Amparo a Pesquisa do Estado de São Paulo (Brasil). The second author wishes to thank the Departament de Matem`atiques de la Universitat Jaume I for support from Pla 2009 de Promoció de la Investigació, Fundació Bancaixa, Castelló, during the preparation of the final version of this paper.
dc.description.upvformatpfin13es_ES
dc.description.upvformatpinicio1es_ES
dc.description.volume12
dc.identifier.doi10.4995/agt.2011.1695
dc.identifier.eissn1989-4147
dc.identifier.issn1576-9402
dc.identifier.urihttps://riunet.upv.es/handle/10251/86961
dc.languageIngléses_ES
dc.publisherUniversitat Politècnica de València
dc.relation.ispartofApplied General Topology
dc.relation.projectIDinfo:eu-repo/grantAgreement/SEP//PIFI%2F34536-55/
dc.relation.publisherversionhttps://doi.org/10.4995/agt.2011.1695es_ES
dc.relation.references10.4995/agt.2004.1972es_ES
dc.relation.references10.1016/j.topol.2006.08.003es_ES
dc.relation.references10.2307/2041624es_ES
dc.relation.references10.1016/0166-8641(93)90103-Kes_ES
dc.relation.references10.1215/S0012-7094-72-03948-8es_ES
dc.rightsReconocimiento - No comercial - Sin obra derivada (by-nc-nd)es_ES
dc.rights.accessRightsAbiertoes_ES
dc.subjectLattice of T1-topologieses_ES
dc.subjectPoset of T3-topologieses_ES
dc.subjectUpper topologyes_ES
dc.subjectLower topologyes_ES
dc.subjectR-closed spacees_ES
dc.subjectR-minimal spacees_ES
dc.subjectSubmaximal spacees_ES
dc.subjectMaximal R-closed spacees_ES
dc.subjectDispersed spacees_ES
dc.titleThe structure of the poset of regular topologies on a setes_ES
dc.typeArtículoes_ES
dc.type.versioninfo:eu-repo/semantics/publishedVersiones_ES
dspace.entity.typePublication
upv.uuid108473ce-8767-4e93-a80b-9f38944d86b5es_ES

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Applied General Topology - Vol 12, No 1 (2011)