Straight nearness spaces

Autor: H. L. Bentley, R.G. Ori
Rok vydání: 2016
Předmět:
Zdroj: Quaestiones Mathematicae; Vol 39, No 6 (2016); 815-829
ISSN: 1727-933X
1607-3606
DOI: 10.2989/16073606.2016.1167136
Popis: 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. Keywords: Straight space, nearness space, continuous map, uniformly continuous map, connectedness, uniform local connectedness, final sinks
Databáze: OpenAIRE
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