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Zbl 1030.54014
Rodríguez-López, Jesús; Romaguera, Salvador
Wijsman and hit-and-miss topologies of quasi-metric spaces. (English)
[J] Set-Valued Anal. 11, No.4, 323-344 (2003). ISSN 0927-6947; ISSN 1572-932X/e

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.
[A.A.Ivanov (St.Peterburg)]

MSC 2000:: *54E15 Uniform structures and generalizations
54B20 Hyperspaces
54A10 Several topologies on one set
54E30 Moore spaces

Keywords: (Hausdorff) quasi-pseudo-metric; (proximal) hit-and-miss topologies; Wijsman topology; Vietoris topology; uniformly Urysohn family; far Urysohn family

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