AI 中文总结
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。
AI 中文摘要
设\(\mathscr{L}\)为林德洛夫空间类且在有限积下封闭。本文证明，若\(G\in\mathscr{L}\)是强拓扑回旋群，则\(G\)是值域可度量化的。还证明，若\(H\)是强拓扑回旋群\(G\in\mathscr{L}\)的强子回旋群，则商空间\(G/H\)中的每个紧致\(G_\delta\)集是杜根吉的。最后，对于任意强拓扑回旋群\(G\)及其闭强子回旋群\(N\)，若\(G\in\mathscr{L}\)且商空间\(G/N\)是局部紧致的，则不等式\(w(G/N)\leq c\)等价于\(G/N\)的可分性。我们的结果将文献中拓扑群的经典结果扩展到了强拓扑回旋群类。
英文摘要
Let $\mathscr{L}$ be the class of Lindelöf spaces such that $\mathscr{L}$ is closed under finite products. In this paper, we prove that if $G \in \mathscr{L}$ is a strongly topological gyrogroup, then $G$ is range-metrizable. Furthermore, we prove that if $H$ is a strong subgyrogroup of a strongly topological gyrogroup $G \in \mathscr{L}$, then every compact $G_δ$-set in the quotient space $G/H$ is Dugundji. Finally, for any strongly topological gyrogroup $G$ and any closed strong subgyrogroup $N$ of $G$, if $G \in \mathscr{L}$ and the quotient space $G/N$ is locally compact, then the inequality $w(G/N) \leq c$ is equivalent to the separability of $G/N$. Our results extend the classical results from topological groups to the class of strongly topological gyrogroups in the literature.
Comments18 pages
