A note on isomorphic groups and nonhomeomorphic spaces
type: Item
instance of: scholarly article
title: A note on isomorphic groups and nonhomeomorphic spaces
zbMATH Open document ID: 0929.54015
DOI: 10.1023/A:1006636108100
published in: Acta Mathematica Hungarica
publication date: 1999-12-08T00:00:00Z
review text: Let \(X\) be a topological space, \(\mathcal G(X)\) the group of autohomeomorphisms of \(X\), and \(2^X\) the hyperspace of nonempty closed subsets of \(X\) endowed with the lower semifinite topology. The main result of this note says that if \(X\) is a Tychonov space, then there is a natural isomorphism between \(\mathcal G(X)\) and \(\mathcal G(2^X)\). Moreover, this isomorphism induces a bijection between the sets of dynamical systems on \(X\) and on \(2^X\).
Mathematics Subject Classification ID: 54C40
Mathematics Subject Classification ID: 54H15
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 1376166
zbMATH Keywords: group of autohomeomorphisms
zbMATH Keywords: lower semifinite topology
zbMATH Keywords: dynamical system
author: Eduardo Cuchillo-Ibáñez
author: Manuel A. Morón
author: Francisco R. Ruiz del Portal
reviewed by: Andrzej Nowak
MaRDI profile type: Publication
full work available at URL: a:1006636108100
OpenAlex ID: W2153388540
description: scientific article; zbMATH DE number 1376166