论文标题
在紧凑的统一复发子组上
On compact uniformly recurrent subgroups
论文作者
论文摘要
让一个$γ$在同质形态上以同型，$ 2^m $表示$ M $的封闭子集的一组$ 2^m $表示，以$ m $的范围$ m $ $γ$进行。我们将$ 2^m $赋予Chabauty拓扑，该拓扑紧凑，并承认同构的天然$γ$ - action。我们表明，对于每一个最小的$γ$ invariant封闭子集$ \ MATHCAL y $ $ 2^m $，由紧凑型组成，Union $ \ bigCup \ Mathcal {y} \ subset m $紧凑闭合。 作为一种应用，我们推断出，局部紧凑型组的每个紧凑型均匀复发子组都包含在紧凑的正常亚组中。这概括了ušakov在归一化量紧凑的紧凑型亚组上的结果。
Let a group $Γ$ act on a paracompact, locally compact, Hausdorff space $M$ by homeomorphisms and let $2^M$ denote the set of closed subsets of $M$. We endow $2^M$ with the Chabauty topology, which is compact and admits a natural $Γ$-action by homeomorphisms. We show that for every minimal $Γ$-invariant closed subset $\mathcal Y$ of $2^M$ consisting of compact sets, the union $\bigcup \mathcal{Y}\subset M$ has compact closure. As an application, we deduce that every compact uniformly recurrent subgroup of a locally compact group is contained in a compact normal subgroup. This generalizes a result of Ušakov on compact subgroups whose normalizer is compact.
