Structure of locally compact groups with metrizable connected components up to negligible subsets
type: Item
instance of: scholarly article
title: Structure of locally compact groups with metrizable connected components up to negligible subsets
zbMATH Open document ID: 0638.22003
DOI: 10.1007/BF01194023
author: Dietrich Helmer
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: It is shown that, after removal of a suitable negligible subset N, a locally compact group G with non-trivial metrizable connected components is of simple topological structure, namely, a product of a discrete space, the space of irrationals, and a Cantor spaces. N can be chosen so as to respect the algebraic and topological structure of G and its Haar measure. Consequently, such a group G has a large supply of \(G_{\delta}\)-subsets of Cantor type. Some of the results have analogues in coset spaces G/H.
Mathematics Subject Classification ID: 22D05
zbMATH DE Number: 4040189
zbMATH Keywords: locally compact groups with metrizable connected components
zbMATH Keywords: topological structure up to negligible subset
zbMATH Keywords: homeomorphy of \(G_{\delta }\)- subspaces in coset space
zbMATH Keywords: product spaces
zbMATH Keywords: abundance of Cantor subspaces
zbMATH Keywords: Haar measure
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4040189