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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:
54E15Uniform structures and generalizations
54B20Hyperspaces (general topology)
54A10Several topologies on one set
54E30Moore spaces