Proximal Hypertopologies Revisited |
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Authors: | R Lowen and M Sioen |
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Institution: | (1) Departement Wiskunde en Informatica, Universiteit Antwerpen, Groenenborgerlaan 171, 2020 Antwerp, Belgium |
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Abstract: | It is the aim of this paper to prove that for an arbitrary metric space (X,d) and a set of nonempty closed subsets of X which contains all singletons and which is closed under enlargements, we can construct a canonical approach distance on the hyperspace CL(X), having the -proximal topology (resp. the Hausdorff metric) as its topological (resp. p-metric) coreflection. We investigate some properties like, e.g., compactness and completeness of the introduced approach structures. In this way we obtain results which generalize their classical counterparts for proximal hit-and-miss hypertopologies. We also give a characterization of the completion of the introduced approach spaces. |
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Keywords: | hyperspace proximal topology bounded proximal topology ball proximal topology Hausdorff metric approach space distance coreflection measure of compactness completeness completion |
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