Rodríguez López, J.; Sanchez Granero, MA. (2011). Some properties of bornological convergences. Topology and its Applications. 158(1):101-117. https://doi.org/10.1016/j.topol.2010.10.009
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Title:
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Some properties of bornological convergences
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Author:
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Rodríguez López, Jesús
Sanchez Granero, Miguel Angel
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UPV Unit:
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Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
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Issued date:
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Abstract:
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We study some basic properties of the so-called bornological convergences in the realm of quasi-uniform spaces. In particular, we revisit the results about when these convergences are topological by means of the use of ...[+]
We study some basic properties of the so-called bornological convergences in the realm of quasi-uniform spaces. In particular, we revisit the results about when these convergences are topological by means of the use of pretopologies. This yields a presentation of the bornological convergences as a certain kind of hit-and-miss pretopologies. Furthermore, we characterize the precompactness and total boundedness of the natural quasi-uniformities associated to these convergences. We also obtain an extension of the classical result of Künzi and Ryser about the compactness of the topology generated by the Hausdorff quasi-uniformity to this framework. © 2010 Elsevier B.V.
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Subjects:
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Bornological convergence
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Compactness
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Precompactness
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Topologicity
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Copyrigths:
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Reserva de todos los derechos
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Source:
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Topology and its Applications. (issn:
0166-8641
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DOI:
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10.1016/j.topol.2010.10.009
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Publisher:
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Elsevier
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Publisher version:
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http://dx.doi.org/10.1016/j.topol.2010.10.009
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Project ID:
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info:eu-repo/grantAgreement/MICINN//MTM2009-12872-C02-01/ES/Construccion De Casi-Metricas Fuzzy, De Distancias De Complejidad Y De Dominios Cuantitativos. Aplicaciones/
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Thanks:
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The authors acknowledge the support of the Spanish Ministry of Science and Innovation grant MTM2009 12872 C02 01
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Type:
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Artículo
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