Quasi-metric spaces, quasi-metric hyperspaces and uniform local compactness
Quasi-metric spaces, quasi-metric hyperspaces and uniform local compactness
A quasi-uniform space \((X,{\mathcal U})\) is uniformly locally compact provided that there exists \(V\in{\mathcal U}\) such that for each \(x\in X\), \(\overline{V(x)}\) is locally compact. A quasi-metric space \((X,d)\) is uniformly locally compact provided that the quasi-uniformity generated by \(d\) is uniformly locally compact. The authors establish that every locally compact quasi-metrizable Moore space admits a uniformly locally compact strong quasi-metric. They also prove results about uniformly locally compact quasi-metric hyperspaces.
- University of Trieste Italy
Uniform structures and generalizations, Metric spaces, metrizability, Hyperspaces in general topology, 54B20, locally compact quasi-metrizable Moore space, Compact (locally compact) metric spaces, 54E35, 54E45
Uniform structures and generalizations, Metric spaces, metrizability, Hyperspaces in general topology, 54B20, locally compact quasi-metrizable Moore space, Compact (locally compact) metric spaces, 54E35, 54E45
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