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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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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

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Título: The structure of the poset of regular topologies on a set
Autor: Alas, Ofelia T. Wilson, Richard G.
Fecha difusión:
Resumen:
[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 ...[+]
Palabras clave: 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
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2011.1695
Editorial:
Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2011.1695
Código del Proyecto:
info:eu-repo/grantAgreement/SEP//PIFI%2F34536-55/
Agradecimientos:
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 ...[+]
Tipo: 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

M. Berri, J. Porter and R. M. Stephenson, A survey of minimal topological spaces, Proc. Kanpur Conference, 1968.

C. Costantini, On some questions about posets of topologies on a fixed set, Topology Proc. 32 (2008), 187–225.

R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.

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.

Hechler, S. H. (1976). Two R-Closed Spaces Revisited. Proceedings of the American Mathematical Society, 56(1), 303. doi:10.2307/2041624

R. E. Larson and W. J. Thron, Covering relations in the lattice of T1-topologies, Trans. Amer. Math. Soc. 168 (1972), 101–111.

J. Porter and R. G. Woods, Extensions and Absolutes of Topological Spaces, Springer Verlag, New York, 1987.

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