Topological Gyrogroups with Fréchet–Urysohn Property and $$\omega ^{\omega }$$-Base

Abstract

The concept of topological gyrogroups is a generalization of a topological group. In this work, ones prove that a topological gyrogroup G is metrizable iff G has an {\omega}{\omega}-base and G is Frechet-Urysohn. Moreover, in topological gyrogroups, every (countably, sequentially) compact subset being strictly (strongly) Frechet-Urysohn and having an {\omega}{\omega}-base are all weakly three-space properties with H a closed L-subgyrogroup