Weak countability axioms on the quotient spaces of topological gyrogroups

In this paper, we mainly prove that if $H$ is a closed strong subgyrogroup of a strongly topological gyrogroup $G$ and $H$ is neutral, then (1) $G\mathrm{/}H$ is biradial if and only if $G\mathrm{/}H$ is nested; (2) $G\mathrm{/}H$ is metrizable if and only if $G\mathrm{/}H$ is a biradial space with countable pseudocharacter; (3) $G\mathrm{/}H$ is metrizable if and only if $G\mathrm{/}H$ has countable $cn$-character, given that $G\mathrm{/}H$ has the Baire property.