  Topological gyrogroups, with a weaker algebraic structure without associative
law, have been investigated recently. We prove that each $T_{0}$-strongly
topological gyrogroup is completely regular. We also prove that every
$T_{0}$-strongly topological gyrogroup with a countable pseudocharacter is
submetrizable. Finally, we prove that the left coset space $G/H$ is
submetrizable if $H$ is an admissible $L$-subgyrogroup of a $T_{0}$-strongly
topological gyrogroup $G$.
