Coincidence of Vietoris and Wijsman Topologies: A New Proof


Autoria(s): Holá, L’.
Data(s)

29/11/2009

29/11/2009

1997

Resumo

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.

Identificador

Serdica Mathematical Journal, Vol. 23, No 3-4, (1997), 363p-366p

1310-6600

http://hdl.handle.net/10525/593

Idioma(s)

en

Publicador

Institute of Mathematics and Informatics Bulgarian Academy of Sciences

Palavras-Chave #Vietoris Topology #Wijsman Topology #Metric Space #Compact Space
Tipo

Article