A universal topological group with countable base
type: Item
instance of: scholarly article
title: A universal topological group with countable base
zbMATH Open document ID: 0608.22003
DOI: 10.1007/BF01077284
publication date: 1986-01-01T00:00:00Z
review text: If \(Q\) is the Hilbert cube and \(\Aut Q\) is the group of all homeomorphisms from \(Q\) to itself with the compact-open topology then the author proves the following theorem: Any topological group with countable basis is topologically isomorphic to some subgroup of the group \(\Aut Q\). The consequence is that there exists a separable Banach space \(E\) such that any topological group with countable basis is isomorphic to some subgroup of the group of all linear isometries on \(E\). It holds for \(E=C(Q)\).
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 3983508
zbMATH Keywords: universal topological group
zbMATH Keywords: Hilbert cube
zbMATH Keywords: countable basis
zbMATH Keywords: separable Banach space
author: Vladimir V. Uspenskij
reviewed by: Bohumil František Šmarda
MaRDI profile type: Publication
cites work: The homeomorphism group of a compact Hilbert cube manifold is an ANR
cites work: Q4060144
full work available at URL: https://doi.org/10.1007/bf01077284
OpenAlex ID: W2171095011
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3983508