标题： 具有合适集的强拓扑可排序的陀螺群 显示英文标题

标题： Strongly topologically orderable gyrogroups with a suitable set

摘要： 一个拓扑平移群 $G$ 的离散子集 $S$ 被称为 {\it 适合的集合} 对于 $G$，如果 $S\cup \{1\}$ 是闭的，并且由 $S$ 生成的子平移群在 $G$中是稠密的，其中 $1$ 是 $G$的单位元。 在本文中，我们主要证明每个强拓扑可序的环群要么是度量化的，要么在单位元处有一个全序局部基$\mathcal{H}$，该局部基由闭开$L$-环子群组成，使得$gyr[x, y](H)=H$对于任何$x, y\in G$和$H\in \mathcal{H}$成立。 此外，我们证明每个强拓扑可序的环群都是遗传仿紧致的。 此外，我们证明每个局部紧致或不是完全不连通的强拓扑可序的环群包含一个合适集。 最后，我们证明如果一个强拓扑可序的环群有一个（闭）合适集，那么它的稠密子环群也具有一个（闭）合适集。 显示英文摘要

摘要： A discrete subset $S$ of a topologically gyrogroup $G$ is called a {\it suitable set} for $G$ if $S\cup \{1\}$ is closed and the subgyrogroup generated by $S$ is dense in $G$, where $1$ is the identity element of $G$. In this paper, we mainly prove that every strongly topologically orderable gyrogroup is either metrizable or has a totally ordered local base $\mathcal{H}$ at the identity element, consisting of clopen $L$-gyrosubgroups, such that $gyr[x, y](H)=H$ for any $x, y\in G$ and $H\in \mathcal{H}$. Moreover, we prove that every strongly topologically orderable gyrogroup is hereditarily paracompact. Furthermore, we show that every locally compact or not totally disconnected strongly topologically orderable gyrogroup contains a suitable set. Finally, we prove that if a strongly topologically orderable gyrogroup has a (closed) suitable set, then its dense subgyrogroup also has a (closed) suitable set.