Quotient with respect to admissible $L$-subgyrogroups

Strongly Topological Gyrogroups and Quotient With Respect to L-subgyrogroups

In this paper, some generalized metric properties in strongly topological gyrogroups are studied.

Quotient spaces with strong subgyrogroups

In this paper, we mainly investigate the quotient spaces G/H when G is a strongly topological gyrogroup and H is a strong subgyrogroup of G. It is shown that if G is a strongly topological gyrogroup, H is a closed strong subgyrogroup of G and H is inner neutral, then the quotient space G/H is first-countable if and only if G/H is a bisequential space if and only if G/H is a weakly first-countable space if and only if G/H is a csf-countable and sequential a7-space. Moreover, it is shown that if H is a locally compact metrizable strong subgyrogroup of G and the quotient space G/H is sequential, …

Quotients with respect to strongly $L$-subgyrogroups

A topological gyrogroup is a gyrogroup endowed with a compatible topology such that the multiplication is jointly continuous and the inverse is continuous. In this paper, we study the quotient gyrogroups in topological gyrogroups with respect to strongly $L$-subgyrogroups, and prove that let $(G, τ,\oplus)$ be a topological gyrogroup and $H$ a closed strongly $L$-subgyrogroup of $G$, then the natural homomorphism $π$ from a topological gyrogroup $G$ to its quotient topology on $G/H$ is an open and continuous mapping, and $G/H$ is a homogeneous $T_1$-space. We also establish that for a locally …

林德洛夫强拓扑回旋群商空间的特征

Characterizations of quotient spaces for Lindelöf strongly topological gyrogroups

研究林德洛夫强拓扑回旋群商空间的特征，证明了若\(G\in\mathscr{L}\)是强拓扑回旋群则\(G\)值域可度量化，还得出\(G/H\)中紧致\(G_\delta\)集是杜根吉的等结论，将拓扑群经典结果扩展到强拓扑回旋群。

Submetrizability of strongly topological gyrogroups

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 $G$.

A class of quotient spaces in strongly topological gyrogroups

Quotient space is a class of the most important topological spaces in the research of topology. In this paper, we show that if G is a strongly topological gyrogroup with a symmetric neighborhood base U at 0 and H is an admissible subgyrogroup generated from U , then G/H is first-countable if and only if it is metrizable. Moreover, if H is neutral and G/H is Frechet-Urysohn with an ωω-base, then G/H is first-countable. Therefore, we obtain that if H is neutral, then G/H is metrizable if and only if G/H is Frechet-Urysohn with an ωω-base. Finally, it is shown that if H is neutral, π\c{hi}(G/H) =…