Inductive limit of general linear groups
type: Item
instance of: scholarly article
title: Inductive limit of general linear groups
zbMATH Open document ID: 0939.22003
author: Aiichi Yamasaki
published in: Journal of Mathematics of Kyoto University
publication date: 2000-07-05T00:00:00Z
review text: The main results of the paper are: (i) For the topology induced from the inductive locally convex vector topology of \(M(\Lambda)\), \(GL(\Lambda)\) is isomorphic to \(C(X,GL(C))\) as topological groups. (ii) \(G\) becomes a topological group with the inductive limit topology as topological spaces if \(\forall n\), \(\exists U\), \(\exists m>n\) such that \(\overline U^{(m)}\) is compact, where \(U\) is a neighbourhood of 1 and \(\overline U^{(m)}\) is the closure of \(U\) in \(G_m\). (iii) If the injection \(G_n\hookrightarrow G_{n+1}\) is a homeomorphism and \(G_1\) is open in \(G_n\) for all \(n\), then the inductive limit topology is a group topology.
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 20G99
zbMATH DE Number: 1319573
zbMATH Keywords: topological group
zbMATH Keywords: inductive limit topology
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518008
OpenAlex ID: W2152221043
DOI: 10.1215/KJM/1250518008
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description: scientific article; zbMATH DE number 1319573