Topological gyrogroups: generalization of topological groups
type: Item
instance of: scholarly article
title: Topological gyrogroups: generalization of topological groups
zbMATH Open document ID: 1382.22008
author: Watchareepan Atiponrat
published in: Topology and its Applications
publication date: 2017-05-15T00:00:00Z
review text: The author studies topological left automorphic left Bol loops. In the terminology of \textit{A. A. Ungar} [Analytic hyperbolic geometry and Albert Einstein's special theory of relativity. Hackensack, NJ: World Scientific (2008; Zbl 1147.83004)] left automorphic left Bol loops are called gyrogroups. In the paper under review, it is shown that for topological gyrogroups the topological separation axioms \(T_0\) and \(T_3\) are equivalent as they are for topological groups. Besides this some interesting facts about topological gyrogroups are shown.
Mathematics Subject Classification ID: 22A30
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 54H11
zbMATH DE Number: 6715602
zbMATH Keywords: topological monoids
zbMATH Keywords: topological quasigroups
zbMATH Keywords: topological loops
reviewed by: Liudmila Sabinina
MaRDI profile type: Publication
full work available at URL: j.topol.2017.04.004
OpenAlex ID: W2606307651
cites work: Induced topologies for quasigroups and loops
cites work: Each regular paratopological group is completely regular
cites work: Contributions to the Theory of Loops
cites work: Q4801824
cites work: TOPOLOGICAL QUASIGROUPS
cites work: Q5289943
cites work: Topological Loops With Invariant Uniformities
cites work: Topological Right Gyrogroups and Gyrotransversals
cites work: On the notion of gyrogroup
cites work: Topological quasi-group shifts
cites work: The Algebra of Gyrogroups: Cayley’s Theorem, Lagrange’s Theorem, and Isomorphism Theorems
cites work: Gyrogroup actions: a generalization of group actions
cites work: Isomorphism theorems for gyrogroups and L-subgyrogroups.
cites work: Lagrange's Theorem for Gyrogroups and the Cauchy Property
cites work: Introduction to topological groups
cites work: Q5433130
DOI: 10.1016/J.TOPOL.2017.04.004
description: scientific article; zbMATH DE number 6715602