Some properties of bornological convergences |
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Authors: | Jesús Rodríguez-López MA Sánchez-Granero |
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Institution: | a Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain b Area of Geometry and Topology, Faculty of Science, Universidad de Almería, 04120 Almería, Spain |
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Abstract: | 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. |
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Keywords: | Bornological convergence Topologicity Precompactness Compactness |
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