The completeness problem for maximal topological groups
type: Item
instance of: scholarly article
title: The completeness problem for maximal topological groups
zbMATH Open document ID: 0731.22001
DOI: 10.1007/BF01066897
author: Vladimir Arnautov
author: Yevhen Zelenyuk
published in: Ukrainian Mathematical Journal
publication date: 1991-01-01T00:00:00Z
review text: A topological group G is maximal if its topology is maximal in the set of all non-discrete group topologies on G. The question of the existence of maximal non-complete topological groups is considered. One can prove that under CH every infinite abelian group admits a complete maximal group topology. Using the Booth Lemma, the authors construct: (1) a complete maximal group G whose topology is the supremum of an increasing \(2^{\omega}\)-sequence of non-discrete linear metrizable topologies on G (Example 2.2); (2) a non-complete maximal topological group (Example 3.3). The completeness of some topological groups which are close to maximal ones is also considered.
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 54A10
Mathematics Subject Classification ID: 54D35
zbMATH DE Number: 4208398
zbMATH Keywords: maximal non-complete topological groups
zbMATH Keywords: complete maximal group topology
zbMATH Keywords: Booth Lemma
zbMATH Keywords: metrizable topologies
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01066897
OpenAlex ID: W2037290357
description: scientific article; zbMATH DE number 4208398