Wijsman and hit-and-miss topologies of quasi-metric spaces
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.
scientific article; zbMATH DE number 1992539