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 $G$.
Categories: math.GN math.GR