Reconciling proximal convergence with uniform convergence in quasi-metric spaces (Q2744641)
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scientific article; zbMATH DE number 1652730
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Reconciling proximal convergence with uniform convergence in quasi-metric spaces |
scientific article; zbMATH DE number 1652730 |
Statements
4 July 2002
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quasi-pseudo-metric
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proximal topology
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Hausdorff quasi-metric
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lower semi-continuous
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quasi-uniformly continuous
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Reconciling proximal convergence with uniform convergence in quasi-metric spaces (English)
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The reviewer [Trans. Am. Math. Soc. 123, 267-272 (1966; Zbl 0151.29703)] and \textit{G. Beer} [Proc. Am. Math. Soc. 95, 653-658 (1985; Zbl 0594.54007)] showed that a metric space \(X\) is UC (continuity equals uniform continuity) if and only if the Hausdorff metric topology on the graphs of real-valued continuous functions agrees with the topology of uniform convergence. In this paper, the authors extend this result to proximal convergence versus uniform convergence in quasi-metric spaces. There are several other interesting results and extensions and the paper is a valuable addition to the literature on hyperspaces and function spaces.
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0.7985902428627014
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