Extensions of some topological properties in topological gyrogroups

Topological gyrogroups, with a weaker algebraic structure than topological groups, has been studied lately. In this paper, it is shown that (1) if H is a closed L- subgyrogroup of a topological gyrogroup G, then G is connected provided H and G/H are connected; (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; (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. The above results generalize the corresponding results in topological groups [3,18].(c) 2022 Elsevier B.V. All rights reserved.