论文标题
关于强烈的$ l $ -subgyRogroups的商
Quotients with respect to strongly $L$-subgyrogroups
论文作者
论文摘要
拓扑陀螺仪是一个具有兼容拓扑结构的陀螺仪，因此乘法是共同连续的，并且反向是连续的。 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 $ g/h $是一个开放式映射，$ g/h $是均质$ t_1 $ -space。我们还确定，对于本地紧凑型$ l $ -subgyRogroup $ h $的拓扑gyrogroup $ g $，自然商映射$π$ $ g $ $ g $ of商空间$ g/h $是本地完美的映射。这使我们对$ g $的属性如何取决于$ g/h $的属性有一些有趣的结果。拓扑组中的一些经典结果被普遍化。
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 compact strongly $L$-subgyrogroup $H$ of a topological gyrogroup $G$, the natural quotient mapping $π$ of $G$ onto the quotient space $G/H$ is a locally perfect mapping. This leads us to some interesting results on how properties of $G$ depend on the properties of $G/H$. Some classical results in topological groups are generalized.
