  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
