Selections and hyperspace topologies via special metrics
type: Item
instance of: scholarly article
title: Selections and hyperspace topologies via special metrics
zbMATH Open document ID: 0863.54009
DOI: 10.1016/0166-8641(95)00092-5
published in: Topology and its Applications
publication date: 1996-07-03T00:00:00Z
review text: Starting from the well-known result of \textit{R. Engelking}, \textit{R. W. Heath} and \textit{E. Michael} [Invent. Math. 6, 150-158 (1968; Zbl 0167.20504), see also Lect. Notes Math. 171, 8-11 (1970; Zbl 0207.21202)] which says that any zero-dimensional completely metrizable space \(Y\) admits a continuous selection with respect to the Vietoris topology on the collection \({\mathcal F}(Y)\) of all nonempty closed subsets of \(Y\), the author proves that a complete metric space \(Y\) with a non-Archimedean metric \(d\) admits a continuous selection \(f:{\mathcal F}(Y)\to Y\) with respect to the \(d\)-proximal topology, which is continuous also within both Hausdorff and Vietoris topologies on \({\mathcal F}(Y)\).
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 896612
zbMATH Keywords: separable metric
zbMATH Keywords: hyperspace topology
zbMATH Keywords: Vietoris topology
zbMATH Keywords: \(d\)-proximal topology
author: Valentin Gutev
reviewed by: J. Chvalina
MaRDI profile type: Publication
full work available at URL: 0166-8641(95)00092-5
OpenAlex ID: W2010356593
cites work: Q4277838
cites work: Distance functionals and suprema of hyperspace topologies
cites work: Q5646103
cites work: Q4695155
cites work: Topological well-ordering and continuous selections
cites work: Equivalence among hypertopologies
cites work: Q4882379
description: scientific article; zbMATH DE number 896612