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The structure of the poset of regular topologies on a set

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The structure of the poset of regular topologies on a set

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dc.contributor.author Alas, Ofelia T. es_ES
dc.contributor.author Wilson, Richard G. es_ES
dc.date.accessioned 2017-09-11T11:56:55Z
dc.date.available 2017-09-11T11:56:55Z
dc.date.issued 2011-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/86961
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. es_ES
dc.description.sponsorship Research 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.language Inglés es_ES
dc.publisher Universitat Politècnica de València
dc.relation.ispartof Applied General Topology
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Lattice of T1-topologies es_ES
dc.subject Poset of T3-topologies es_ES
dc.subject Upper topology es_ES
dc.subject Lower topology es_ES
dc.subject R-closed space es_ES
dc.subject R-minimal space es_ES
dc.subject Submaximal space es_ES
dc.subject Maximal R-closed space es_ES
dc.subject Dispersed space es_ES
dc.title The structure of the poset of regular topologies on a set es_ES
dc.type Artículo es_ES
dc.date.updated 2017-09-11T11:50:31Z
dc.identifier.doi 10.4995/agt.2011.1695
dc.relation.projectID info:eu-repo/grantAgreement/SEP//PIFI%2F34536-55/
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Alas, 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.2011.1695 es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2011.1695 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 13 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 12
dc.description.issue 1
dc.identifier.eissn 1989-4147
dc.contributor.funder Secretaría de Educación Pública, México
dc.contributor.funder Fundação de Amparo à Pesquisa do Estado de São Paulo
dc.contributor.funder Universitat Jaume I
dc.contributor.funder Fundación Bancaja
dc.description.references O. 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.references O. 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.references Alas, 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.2004.1972 es_ES
dc.description.references M. Berri, J. Porter and R. M. Stephenson, A survey of minimal topological spaces, Proc. Kanpur Conference, 1968. es_ES
dc.description.references C. Costantini, On some questions about posets of topologies on a fixed set, Topology Proc. 32 (2008), 187–225. es_ES
dc.description.references R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989. es_ES
dc.description.references L. 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.references Hechler, S. H. (1976). Two R-Closed Spaces Revisited. Proceedings of the American Mathematical Society, 56(1), 303. doi:10.2307/2041624 es_ES
dc.description.references R. 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.references J. Porter and R. G. Woods, Extensions and Absolutes of Topological Spaces, Springer Verlag, New York, 1987. es_ES


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