Extensions of some topological properties in topological gyrogroups
type: Item
instance of: scholarly article
title: Extensions of some topological properties in topological gyrogroups
zbMATH Open document ID: 1504.54028
author: Jing Zhang
author: Qianqian Liang
published in: Topology and its Applications
publication date: 2022-12-08T00:00:00Z
review text: The authors investigate topological gyrogroups that possess a weaker algebraic structure than topological groups. In this paper, it is shown that \begin{itemize} \item[(1)] if \(H\) is a closed \(L\)-subgyrogroup of a topological gyrogroup \(G\), then \(G\) is connected provided \(H\) and \(G/H\) are connected; \item[(2)] if \(H\) is a closed \(L\)-subgyrogroup of a topological gyrogroup \(G\), then \(G\) is totally disconnected provided \(H\) and \(G/H\) are totally disconnected; \item[(3)] if \(H\) is a locally compact metrizable connected and normal subgyrogroup of a topological gyrogroup \(G\), then \(G\) is sequentially connected provided the quotient gyrogroup \(G/H\) is sequentially connected. \end{itemize} The above results generalize the corresponding results in the case of topological groups.
reviewed by: Watchareepan Atiponrat
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 54H99
Mathematics Subject Classification ID: 18A32
Mathematics Subject Classification ID: 54B15
zbMATH DE Number: 7628708
zbMATH Keywords: topological gyrogroups
zbMATH Keywords: quotient spaces
zbMATH Keywords: three spaces properties
zbMATH Keywords: strongly \(L\)-subgyrogroups
MaRDI profile type: Publication
full work available at URL: j.topol.2022.108328
OpenAlex ID: W4307812287
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DOI: 10.1016/J.TOPOL.2022.108328
description: scientific article; zbMATH DE number 7628708