Retractions in hyperspaces.
type: Item
instance of: scholarly article
title: Retractions in hyperspaces.
zbMATH Open document ID: 1036.54002
DOI: 10.1016/S0166-8641(03)00193-7
published in: Topology and its Applications
publication date: 2004-02-03T00:00:00Z
review text: Given a metric continuum \(X\), let \(2^X\), \(C(X)\) and \(C_2(X)\) denote the hyperspaces of all nonempty closed subsets, subcontinua, and closed subsets with at most two components of \(X\), respectively (with the Hausdorff metric). For a fixed point \(p \in X\) the symbols \(2^X_p\), \(C(p,X)\) and \(C_2(p,X)\) denote the subspaces consisting of these elements of the corresponding hyperspaces that contain the point \(p\). The author studies various mappings between these hyperspaces, especially retractions and (strong) deformation retractions. She characterizes contractibility of \(2^X\) and \(C(X)\) as well as local connectedness of \(X\) in terms of the behaviour of these mappings.
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 2037243
zbMATH Keywords: continuum
zbMATH Keywords: hyperspace
zbMATH Keywords: retraction
author: Patricia Pellicer-Covarrubias
reviewed by: Janusz J. Charatonik
MaRDI profile type: Publication
cites work: Hyperspaces of finite subsets which are homeomorphic to \(\aleph _ 0\)- dimensional linear metric spaces
cites work: Q4230677
cites work: Hyperspaces of a Continuum
cites work: Q3869981
cites work: Q4004123
full work available at URL: s0166-8641(03)00193-7
OpenAlex ID: W2045987921
description: scientific article; zbMATH DE number 2037243