Hilbert's fifth problem: Review
type: Item
instance of: scholarly article
title: Hilbert's fifth problem: Review
zbMATH Open document ID: 1004.57029
DOI: 10.1023/A:1011323915468
published in: Journal of Mathematical Sciences (New York)
publication date: 2002-10-30T00:00:00Z
review text: The author gives an overview of results concerning Hilbert's fifth problem which can be stated as follows: Let \(G\) be a locally Euclidean topological group, let \(M\) be a locally Euclidean topological space, i.e., \(M\) is a topological manifold, and let a continuous action \(\Phi:G\times M\to M\) of \(G\) on \(M\) be given. Is it then always possible to choose the local coordinates in \(G\) and \(M\) in such a way that the action \(\Phi\) becomes real analytic? In other words, is it possible to give the topological manifolds \(G\) and \(M\) real analytic structures such that \(\Phi\) becomes real analytic?
Mathematics Subject Classification ID: 57S99
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 22E99
Mathematics Subject Classification ID: 57-03
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 57-02
zbMATH DE Number: 1821781
zbMATH Keywords: real analytic action
zbMATH Keywords: Lie group
author: Soeren Illman
MaRDI profile type: Publication
full work available at URL: a:1011323915468
OpenAlex ID: W54846295
description: scientific article; zbMATH DE number 1821781