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Thoughts on Quotient-fine Nearness Frames

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Abstract

We characterize nearness frames whose completions are fine (we call them quotient-fine), and show that the subcategory QfNFrm they form is reflective in the category of strong nearness frames. The resulting functor commutes with the completion functor. QfNFrm is isomorphic to the subcategory of the functor category (RegFrm)2 given by the dense onto \(h\colon M\to L\), where 2 denotes the category with only two objects and exactly one morphism between them.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of South Africa, P.O. Box 392, 0003, Unisa, South Africa

    Themba Dube

  2. Department of Mathematics, University of Namibia, P.O. Box 13301, Windhoek, Namibia

    Martin M. Mugochi

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  1. Themba Dube
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  2. Martin M. Mugochi
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Correspondence to Themba Dube.

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Dube, T., Mugochi, M.M. Thoughts on Quotient-fine Nearness Frames. Appl Categor Struct 19, 511–521 (2011). https://doi.org/10.1007/s10485-009-9216-1

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  • DOI: https://doi.org/10.1007/s10485-009-9216-1

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