Characterizations of compact ordinal spaces via continuous selections
type: Item
instance of: scholarly article
title: Characterizations of compact ordinal spaces via continuous selections
zbMATH Open document ID: 0926.54011
DOI: 10.1016/S0166-8641(97)00243-5
published in: Topology and its Applications
publication date: 1999-11-29T00:00:00Z
review text: Let \(X\) be a compact Hausdorff space. It is proved, that \(X\) is homeomorphic to an ordinal space if and only if there exists a continuous selection \(f:{\mathcal F}(X)\to X\) on the hyperspace \({\mathcal F}(X)\) of closed nonempty subsets of \(X\) such that \(f(F)\) is an isolated point of \(F\) for every \(F\in {\mathcal F}(X)\). The paper contains also examples and a problem concerning the characterization of spaces of ordinals via continuous selections under the condition of local compactness.
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54F65
zbMATH DE Number: 1307906
zbMATH Keywords: ordinal space
author: Seiji Fujii
author: T. Nogura
reviewed by: Włodzimierz Ślęzak
MaRDI profile type: Publication
cites work: Q5646103
cites work: Topological well-ordering and continuous selections
cites work: Topologies on Spaces of Subsets
cites work: Q4882379
cites work: Selections and Orderability
cites work: Characterizations of intervals via continuous selections
cites work: Q3425662
description: scientific article; zbMATH DE number 1307906