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Hyperspaces and function spaces. (English) Zbl 0717.54005
In this survey article, the author omits all proofs, seeking instead to motivate various lines of research, most of which are related to the author’s work over a quarter century. There is a massive collection of 90 numbered results. The range of topics is indicated by the sections into which the paper is divided: 1. The Locally Finite Hypertopology; 2. Proximal Hypertopologies; 3. Generalized uniformities and the Locally Finite Topology; 4. Graph Topology [for a function space]; 5. Graph Topologies [corresponding to hypertopologies]; 6. Proximal Graph Topologies; 7. Connected and Connectivity Function Spaces; 8. Proximal and Nearness Convergence; 9. Topological and Uniform Convergence; 10. Wijsman Convergence. There is a list of general areas for future investigation and a substantial bibliography.
Reviewer: M.Michael

MSC:
54B20 Hyperspaces in general topology
54C35 Function spaces in general topology
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
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