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On Strict Extensions of Nearness Spaces

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Abstract

Strict extensions of nearness spaces are constructed as spaces of round Cauchy filters. Morita's simple extension is identified as the strict extension generated by Morita-generated filters. Carlson's B-completeness is compared with Herrlich completeness and completeness of Morita T-uniformities. The three completeness concepts are shown to be equivalent in regular nearness spaces.

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Authors and Affiliations

  1. St Edmund Hall, Oxford, OX1 4AR, U.K.

    P. J. Collins

  2. Merton College, Oxford, OX1 4JD, U.K.

    C. A. Hendrie

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  1. P. J. Collins
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  2. C. A. Hendrie
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Collins, P.J., Hendrie, C.A. On Strict Extensions of Nearness Spaces. Applied Categorical Structures 8, 435–446 (2000). https://doi.org/10.1023/A:1008614929530

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  • DOI: https://doi.org/10.1023/A:1008614929530

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