G. Di. Maio, L. Hola, E. Meccariello
Notes on hit-and-miss topologies
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 52, 19-32 (1998)
54B20 Hyperspaces
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54E35 Metric spaces, metrizability
Abstract: We give necessary conditions for normality of \DD\!-topologies, where \DD is
stable under closed subsets. We have a complete solution of metrizability
of proximal topology in uniform setting.
Keywords: Hit-and-miss, proximal, hypertopology, bounded, totally bounded, Urysohn family, Keesling family, uniform space, compatible metric, metrizability