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Wijsman and hit-and-miss topologies of quasi-metric spaces. (English) Zbl 1030.54014
The authors study the relationship between the Wijsman topology and (proximal) hit-and-miss topologies on hyperspaces of quasi-metric spaces. They establish the equivalence of these hypertopologies in terms of Urysohn families of sets. They also show that for quasi-metric spaces \((X,d)\), the Hausdorff extended quasi-pseudo-metric is compatible with the Wijsman hypertopology if and only if \(d^{-1}\) is hereditarily precompact.

MSC:
54E15 Uniform structures and generalizations
54B20 Hyperspaces in general topology
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54E30 Moore spaces
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