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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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