  A topological gyrogroup is a gyrogroup endowed with a topology such that the
binary operation is jointly continuous and the inverse mapping is also
continuous. In this paper, it is proved that if $G$ is a sequential topological
gyrogroup with an $\omega^{\omega}$-base, then $G$ has the strong Pytkeev
property. Moreover, some equivalent conditions about $\omega^{\omega}$-base and
strong Pytkeev property are given in Baire topological gyrogroups. Finally, it
is shown that if $G$ is a strongly countably complete strongly topological
gyrogroup, then $G$ contains a closed, countably compact, admissible
subgyrogroup $P$ such that the quotient space $G/P$ is metrizable and the
canonical homomorphism $\pi :G\rightarrow G/P$ is closed.
