Weakly first-countability in strongly topological gyrogroups

Abstract

In this note, it is proved that (1) if (G,τ,⊕) is a strongly topological gyrogroup and H is a closed strong subgyrogroup of G, then G/H is κ-Fréchet-Urysohn if and only if G/H is strongly κ-Fréchet-Urysohn under the condition that H is neutral; (2) let H be a closed strong subgyrogroup of a strongly topological gyrogroup(G,τ,⊕), then the equality Δ(G/H)=ψ(G/H) holds when H is neutral; (3) if (G,τ,⊕) is a sequential strongly topological gyrogroup having a point-countable k-network, then G is metrizable or a topological sum of cosmic subspaces. There results improve the related results in topological groups.