Extensions of some topological properties in topological gyrogroups
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.
scientific article; zbMATH DE number 7628708
scientific article