Straight nearness spaces

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 st...

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Bibliographic Details
Published in:Quaestiones mathematicae 2016-09, Vol.39 (6), p.815-829
Main Authors: Bentley, H.L., Ori, R.G.
Format: Article
Language:English
Subjects:
connectedness
continuous map
final sinks
nearness space
Straight space
uniform local connectedness
uniformly continuous map
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Summary: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.
ISSN:1607-3606
1727-933X
DOI:10.2989/16073606.2016.1167136