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Volume 23 Number 3-4 >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/593

Title: Coincidence of Vietoris and Wijsman Topologies: A New Proof
Authors: Holá, L’.
Keywords: Vietoris Topology
Wijsman Topology
Metric Space
Compact Space
Issue Date: 1997
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 23, No 3-4, (1997), 363p-366p
Abstract: Let (X, d) be a metric space and CL(X) the family of all nonempty closed subsets of X. We provide a new proof of the fact that the coincidence of the Vietoris and Wijsman topologies induced by the metric d forces X to be a compact space. In the literature only a more involved and indirect proof using the proximal topology is known. Here we do not need this intermediate step. Moreover we prove that (X, d) is boundedly compact if and only if the bounded Vietoris and Wijsman topologies on CL(X) coincide.
URI: http://hdl.handle.net/10525/593
ISSN: 1310-6600
Appears in Collections:Volume 23 Number 3-4

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