Hyperspaces of Keller compacta and their orbit spaces
type: Item
instance of: scholarly article
title: Hyperspaces of Keller compacta and their orbit spaces
zbMATH Open document ID: 1341.57015
author: Sergey A. Antonyan
author: Natalia Jonard-Pérez
author: Saúl Juárez-Ordóñez
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-03-27T00:00:00Z
review text: This is a nice application of infinite-dimensional topology to topological dynamics. The authors prove among other things that for a compact group \(G\) acting affinely on a centrally symmetric Keller cube \(K\), the orbit spaces \(2^K/G\) and \(cc(K)/G\) are both homeomorphic to the Hilbert cube. Here \(2^K\) denotes the hyperspace of all non-empty closed subsets of \(K\) endowed with the Vietoris topology. Moreover, \(cc(K)\) denotes its subspace consisting of all nonempty closed and convex subsets of \(K\). The Hilbert cube \(Q\) is a centrally symmetric Keller cube, so this result applies to \(Q\). The paper ends with some interesting unsolved problems.
reviewed by: Jan van Mill
Mathematics Subject Classification ID: 57N20
Mathematics Subject Classification ID: 37C85
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 6420108
zbMATH Keywords: Keller compactum
zbMATH Keywords: infinite-dimensional convex set
zbMATH Keywords: hyperspace
zbMATH Keywords: affine group
zbMATH Keywords: orbit space
zbMATH Keywords: \(Q\)-manifold
MaRDI profile type: Publication
full work available at URL: j.jmaa.2013.10.076
OpenAlex ID: W2024657028
cites work: Q4748843
cites work: Q3802239
cites work: RETRACTION PROPERTIES OF AN ORBIT SPACE
cites work: Q4523067
cites work: West’s problem on equivariant hyperspaces and Banach-Mazur compacta
cites work: Affine group acting on hyperspaces of compact convex subsets of \({\mathbb R}^{n}\)
cites work: Estimated extension theorem, homogeneous collections and skeletons and their applications to topological classification of linear metric spaces and convex sets
cites work: Q4060144
cites work: Q5658847
cites work: Q4078838
cites work: The homeomorphism group of a compact Hilbert cube manifold is an ANR
cites work: Some Topological Properties of Convex Sets
cites work: Q5614773
cites work: Q3812929
cites work: Hyperspaces of compact convex sets
cites work: Q4230677
cites work: The classification of 𝐺-spaces
cites work: The Contractibility of the Homeomorphism Group of Some Product Spaces by Wong's Method.
cites work: The AR-Property of the spaces of closed convex sets
cites work: ON EQUIVARIANT EMBEDDINGS OFG-SPACES
cites work: Q4119827
cites work: On CE-images of the Hubert cube and characterization of Q-manifolds
DOI: 10.1016/J.JMAA.2013.10.076
description: scientific article; zbMATH DE number 6420108