Straight nearness spaces |
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Authors: | HL Bentley RG Ori |
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Institution: | 1. Department of Mathematics, University of Toledo, Toledo, Ohio 43606 USA.;2. Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa. |
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Abstract: | Straight spaces are spaces for which a continuous map defined on the space which is uniformly continuous on each set of a finite closed cover is then uniformly continuous on the whole space. Previously, straight spaces have been studied in the setting of metric spaces. In this paper, we present a study of straight spaces in the more general setting of nearness spaces. In a subcategory of nearness spaces somewhat more general than uniform spaces, we relate straightness to uniform local connectedness. We investigate category theoretic situations involving straight spaces. We prove that straightness is preserved by final sinks, in particular by sums and by quotients, and also by completions. |
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Keywords: | 54A05 54B30 54E15 54E17 |
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