Haar nonmeasurable partitions of compact groups
type: Item
instance of: scholarly article
title: Haar nonmeasurable partitions of compact groups
zbMATH Open document ID: 0887.22004
published in: Tsukuba Journal of Mathematics
publication date: 1998-05-12T00:00:00Z
review text: The paper deals with some aspects concerning the behaviour of compact groups. Mention must be made of the following results: Theorem 7. Let \(G\) be a nonmetrizable compact group. Then \(G\) can be partitioned into \(|G|\)-many pairwise disjoint dense homogeneously invariant \(\omega\)-bounded subsets each of which is of cardinality \(|G|\) and Haar nonmeasurable with full Haar outer measure. Theorem 8. Every infinite compact group \(G\) can be partitioned into \(|G|\) pairwise disjoint dense nonmeasurable sets of full Haar outer measure. At the end of the paper we find an important corollary, namely: Let \(A\) be an infinite discrete topological space. Then its Stone-Čech compactification \(\beta A\) can be partitioned into a collection of size \(|\beta A|\) pairwise disjoint \(\omega\)-bounded sets each of which is itself of size \(|\beta A|\).
Mathematics Subject Classification ID: 22C05
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54B05
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54B15
zbMATH DE Number: 1102925
zbMATH Keywords: Haar nonmeasurable partitions
zbMATH Keywords: compact groups
zbMATH Keywords: topological space
zbMATH Keywords: Stone-Cech compactification
author: Gerald L. Itzkowitz
author: Dmitri Shakhmatov
reviewed by: Olga Costinescu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496163176
OpenAlex ID: W1637673921
DOI: 10.21099/TKBJM/1496163176
description: scientific article; zbMATH DE number 1102925