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The structure of the poset of regular topologies on a set

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Alas, OT.; Wilson, RG. (2011). The structure of the poset of regular topologies on a set. Applied General Topology. 12(1):1-13. doi:10.4995/agt.2011.1695.

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/86961

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Title: The structure of the poset of regular topologies on a set
Author:
Issued date:
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 ...[+]
Subjects: Lattice of T1-topologies , Poset of T3-topologies , Upper topology , Lower topology , R-closed space , R-minimal space , Submaximal space , Maximal R-closed space , Dispersed space
Copyrigths: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Source:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2011.1695
Publisher:
Universitat Politècnica de València
Publisher version: https://doi.org/10.4995/agt.2011.1695
Thanks:
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 ...[+]
Type: Artículo

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.

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.

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 [+]
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.

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.

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

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Valent, R., & Larson, R. E. (1972). Basic intervals in the lattice of topologies. Duke Mathematical Journal, 39(3), 401-411. doi:10.1215/s0012-7094-72-03948-8

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