On the hyperspace suspension of a continuum.
type: Item
instance of: scholarly article
title: On the hyperspace suspension of a continuum.
zbMATH Open document ID: 1063.54005
author: Raúl Escobedo
author: María de Jesús López
author: Sergio Macías
published in: Topology and its Applications
publication date: 2004-03-14T00:00:00Z
review text: The paper consists of eight sections: 1. Introduction, 2. Definitions, 3. General properties, 4. Aposyndesis, 5. Local connectedness, 6. Cones, 7. A universal map theorem, 8. Hereditarily indecomposable continua. For a continuum \(X\), let \(C(X)\) denote the hyperspace of subcontinua of \(X\) and \({\mathcal F}_{1}(X)\) the space of singletons of \(X\), topologized with the Hausdorff metric. The \textit{hyperspace suspension} \(HS(X)\) is the quotient space \(C(X)/{\mathcal F}_{1}(X)\). The authors prove some properties of this hyperspace, for example: (a) \(HS(X)\) is finitely aposyndetic for each continuum \(X\); (b) if \(F\) is a smooth fan, then \(HS(F)\) is homeomorphic to \(C(F)\); (c) the hyperspace suspension of the Hilbert Cube is homeomorphic to the Hilbert Cube.
reviewed by: Władysław Makuchowski
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 2056821
zbMATH Keywords: aposyndesis
zbMATH Keywords: C-H continuum
zbMATH Keywords: cone
zbMATH Keywords: continuum
zbMATH Keywords: Fan
zbMATH Keywords: hereditarily indecomposable continuum
zbMATH Keywords: hyperspace
zbMATH Keywords: hyperspace suspension
zbMATH Keywords: indecomposable continuum
zbMATH Keywords: smooth fan
zbMATH Keywords: surjective semispan
zbMATH Keywords: suspesion
MaRDI profile type: Publication
full work available at URL: j.topol.2003.08.024
OpenAlex ID: W2399974169
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DOI: 10.1016/J.TOPOL.2003.08.024
description: scientific article; zbMATH DE number 2056821