Rodríguez-López, Jesús; Romaguera, Salvador Wijsman and hit-and-miss topologies of quasi-metric spaces. (English) Zbl 1030.54014 Set-Valued Anal. 11, No. 4, 323-344 (2003). 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. Reviewer: A.A.Ivanov (St.Peterburg) Cited in 7 Documents 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 Keywords:(Hausdorff) quasi-pseudo-metric; (proximal) hit-and-miss topologies; Wijsman topology; Vietoris topology; uniformly Urysohn family; far Urysohn family PDFBibTeX XMLCite \textit{J. Rodríguez-López} and \textit{S. Romaguera}, Set-Valued Anal. 11, No. 4, 323--344 (2003; Zbl 1030.54014)