Weakly first-countability in strongly topological gyrogroups

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...

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Published in:Topology and its applications 2024-06, Vol.350, p.108920, Article 108920
Main Authors: Zhang, Jing, Lin, Kaixiong, Xi, Wenfei
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Language:English
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k-networks
Neutral strong subgyrogroups
Point-countable covers
Sequential spaces
Topological gyrogroups
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description 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.
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subjects k-networks
Neutral strong subgyrogroups
Point-countable covers
Sequential spaces
Topological gyrogroups
title Weakly first-countability in strongly topological gyrogroups
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