Normality and countable paracompactness of hyperspaces of ordinals
type: Item
instance of: scholarly article
title: Normality and countable paracompactness of hyperspaces of ordinals
zbMATH Open document ID: 1116.54006
author: Nobuyuki Kemoto
published in: Topology and its Applications
publication date: 2007-02-09T00:00:00Z
review text: For a space \(X\), \(2^X\) denotes the space consisting of all nonempty closed subsets of \(X\) with the Vietoris topology and \({\mathcal K}(X)\) denotes the subspace of \(2^X\) consisting of all compact subsets of \(X\). The author discusses normality and countable paracompactness of hyperspaces of ordinals and proves the following results: Theorem 5. \({\mathcal K}(\alpha)\) is countably paracompact for all nonzero-ordinals \(\alpha\). Theorem 8. If \(\kappa\) is a regular uncountable cardinal, then \({\mathcal K}(\kappa)\) is normal. The author also discusses the space \(2^X\).
reviewed by: Akihiro Okuyama
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54D20
zbMATH DE Number: 5123618
zbMATH Keywords: normal
zbMATH Keywords: countably paracompact
zbMATH Keywords: hyperspace
zbMATH Keywords: ordinal
zbMATH Keywords: elementary submodel
MaRDI profile type: Publication
full work available at URL: j.topol.2006.04.017
OpenAlex ID: W2048048692
cites work: Q3472092
cites work: Q5847712
cites work: Normality and Properties Related to Compactness in Hyperspaces
cites work: Set theory. An introduction to independence proofs
cites work: Topologies on Spaces of Subsets
cites work: Q3906089
cites work: On spaces of closed subsets
DOI: 10.1016/J.TOPOL.2006.04.017
description: scientific article; zbMATH DE number 5123618