Weak countability axioms on the quotient spaces of topological gyrogroups

TL;DR

This paper investigates conditions under which quotient spaces of topological gyrogroups exhibit properties like biradiality and metrizability, establishing equivalences involving countability axioms and the Baire property.

Contribution

It provides new characterizations of quotient spaces of topological gyrogroups using countability axioms and properties like biradiality and the Baire property.

Findings

$G/H$ is biradial iff it is nested.

$G/H$ is metrizable iff it is biradial with countable pseudocharacter.

$G/H$ is metrizable iff it has countable $cn$-character with Baire property.

Abstract

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) $G/H$ is biradial if and only if $G/H$ is nested; (2) $G/H$ is metrizable if and only if $G/H$ is a biradial space with countable pseudocharacter; (3) $G/H$ is metrizable if and only if $G/H$ has countable $cn$-character, given that $G/H$ has the Baire property.