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 TopologyWijsman TopologyMetric SpaceCompact 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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