The topological structure of Polish groups and groupoids of measure space transformations
type: Item
instance of: scholarly article
title: The topological structure of Polish groups and groupoids of measure space transformations
zbMATH Open document ID: 0851.22001
author: Alexandre I. Danilenko
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1996-11-11T00:00:00Z
review text: Soit \((X,\mu)\) un espace mesuré sans atome et \(\sigma\)-fini. Soit \(\text{Part} (X,\mu)\) le groupoïde des \(\mu\)-isomorphismes d'un sous-ensemble de \(X\) sur un autre sous-ensemble de \(X\), muni de la topologie faible. L'auteur montre que \(\text{Part}(X, \mu)\) est contractile par une homotopie laissant invariant le sous-groupoïde des isomorphismes partiels conservant \(\mu\), ainsi que le groupe \(\text{Aut} (X,\mu)\) des isomorphismes de \((X, \mu)\). Pour un sous-groupe dénombrable \(\Gamma\) de \(\text{Aut}(X, \mu)\), soit \([\Gamma] = \{\theta\in \text{Aut}(X,\mu)/\theta(x) \in \Gamma x\) pour presque tout \(x\}\). L'auteur étudie la contractilité du groupe \([\Gamma]\), muni de la topologie uniforme, ainsi que le type d'homotopie de son normalisateur dans \(\Aut(X,\mu)\).
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 22A22
Mathematics Subject Classification ID: 28D15
Mathematics Subject Classification ID: 46L55
zbMATH DE Number: 878505
zbMATH Keywords: Polish groups
zbMATH Keywords: groupoid
zbMATH Keywords: measure space transformations
reviewed by: Robert Cauty
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195163723
OpenAlex ID: W2111121092
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DOI: 10.2977/PRIMS/1195163723
description: scientific article; zbMATH DE number 878505