论文标题
紧凑的谎言群体隔离到共轭
Compact Lie groups isolated up to conjugacy
论文作者
论文摘要
Hausdorff拓扑组$ G $的紧凑型亚组的$ \ Mathcal S（G）$可以配备越野拓扑。如果存在$ k $的邻居$ \ Mathcal u \ subseteq \ subseteq \ Mathcal s（g）$ k $的紧凑型亚组$ k \ in \ mathcal s（g）$隔离为共轭。在本文中，我们表征了一个孤立组的紧凑型亚组，这些子群是隔离为结合性的。我们的特征仅取决于$ k $的内在结构，环境谎言组$ g $以及$ k $的嵌入到$ g $中是无关紧要的。 此外，我们证明，紧凑型$ g $上的任何连续的同态性能连续到紧凑型谎言组$ h $都会引起$ \ mathcal s（g）$的连续开放地图上$ \ mathcal s（h）$。
The set $\mathcal S(G)$ of compact subgroups of a Hausdorff topological group $G$ can be equipped with the Vietoris topology. A compact subgroup $K\in\mathcal S(G)$ is isolated up to conjugacy if there is a neighborhood $\mathcal U\subseteq\mathcal S(G)$ of $K$ such that every $L\in\mathcal U$ is conjugate to $K$. In this paper, we characterize compact subgroups of a Lie group that are isolated up to conjugacy. Our characterization depends only on the intrinsic structure of $K$, the ambient Lie group $G$ and the embedding of $K$ into $G$ are irrelevant. In addition, we prove that any continuous homomorphism from a compact group $G$ onto a compact Lie group $H$ induces a continuous open map from $\mathcal S(G)$ onto $\mathcal S(H)$.
