Graphs have unique quotient hyperspace \(\mathcal{C}_1^n(X)\)
type: Item
instance of: scholarly article
title: Graphs have unique quotient hyperspace \(\mathcal{C}_1^n(X)\)
zbMATH Open document ID: 1487.54049
author: Ulises Morales-Fuentes
author: Sergio Macías
published in: Topology and its Applications
publication date: 2022-02-09T00:00:00Z
review text: A \textit{continuum} is a compact, connected and nonempty metric space. Given a continuum \(X\) and a positive integer \(n\), the symbol \(C_{n}(X)\) denotes the hyperspace of all non empty, closed subsets of \(X\) having at most \(n\) components, topologized with the Hausdorff metric. Also, the symbol \(C^{1}_{n}(X)\) denotes the quotient space \(C_{n}(X)/C_{1}(X)\). In the paper under review, the authors show that, given a finite graph \(X\) and a continuum \(Y\) such that \(C^{1}_{n}(X)\) and \(C^{1}_{n}(Y)\) are homeomorphic, it holds that \(X\) and \(Y\) are homeomorphic. This result extends work carried out by several authors in the theory of hyperspaces related to the study and characterization of unique hyperspaces.
reviewed by: Javier Sánchez-Martínez
Mathematics Subject Classification ID: 54F16
Mathematics Subject Classification ID: 54B20
zbMATH DE Number: 7471572
zbMATH Keywords: continuum
zbMATH Keywords: hyperspace
zbMATH Keywords: quotient space
MaRDI profile type: Publication
full work available at URL: j.topol.2021.107996
OpenAlex ID: W4206539234
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DOI: 10.1016/J.TOPOL.2021.107996
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description: scientific article; zbMATH DE number 7471572