Finite-valued multiselections
type: Item
instance of: scholarly article
title: Finite-valued multiselections
zbMATH Open document ID: 1365.54012
published in: Topology and its Applications
publication date: 2017-05-18T00:00:00Z
review text: Let \(\mathcal{F}(X)\) be the collection of all nonempty closed subsets of a space \(X\). Each subcollection \(\mathcal{D}\subset\mathcal{F}(X)\) will carry the Vietoris topology \(\tau_{V}\). A space \(X\) is weakly orderable if it has a coarser open interval topology. In the present paper, the author is interested in set-valued selections for hyperspaces. The main results are: Theorem 1.1. Let \(X\) be a connected space which has a \(\tau_{V}\)-continuous multiselection \(\varphi:\mathcal{F}_{n}(X)\rightarrow\mathcal{F}_{n+1}(X)\) for some \(n\geq 1\). Then \(X\) is weakly orderable. Theorem 1.2. Let \(X\) be a connected space which has a \(\tau_{V}\)-continuous multiselection \(\phi:\mathcal{F}(X)\rightarrow\sum(X)\). If \(\varphi\) is not singleton-valued at some element of \(\mathcal{F}(X)\), then \(X\) is compact and orderable.
reviewed by: Zuquan Li
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 54F05
zbMATH DE Number: 6720079
zbMATH Keywords: Vietoris topology
zbMATH Keywords: multiselection
zbMATH Keywords: weak selection
zbMATH Keywords: weak orderability
author: Valentin Gutev
MaRDI profile type: Publication
full work available at URL: j.topol.2017.04.017
OpenAlex ID: W2607356296
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DOI: 10.1016/J.TOPOL.2017.04.017
description: scientific article; zbMATH DE number 6720079