论文标题
$ 0 $二维紧凑型空间的Clopen类型的动作半群
Clopen type semigroups of actions on $0$-dimensional compact spaces
论文作者
论文摘要
我们研究了可数组对紧凑型组的作用的Clopen型半群的某些特性，$ 0 $维度，Hausdorff SpaceX。我们在这种情况下讨论了一些动态比较的特征（其中大多数是在Metrizable的情况下已经知道的）；并证明，对于一个cantor的最小动作$α$，违反组的拓扑完整组$α$承认了一个密集的，本地有限的子组，如果相应的clopen型semigroup是未施加的。我们还讨论了clopen型半群的某些属性，即石chech压缩和可计数基团的通用最小流，并在给定的可数基团在坎托空间的最小作用的空间中对通用特性产生了一些后果。
We investigate some properties of the clopen type semigroup of an action of a countable group on a compact, $0$-dimensional, Hausdorff space X. We discuss some characterizations of dynamical comparison (most of which were already known in the metrizable case) in this setting; and prove that for a Cantor minimal action $α$ of an amenable group the topological full group of $α$ admits a dense, locally finite subgroup iff the corresponding clopen type semigroup is unperforated. We also discuss some properties of clopen type semigroups of the Stone-Čech compactifications and universal minimal flows of countable groups, and derive some consequences on generic properties in the space of minimal actions of a given countable group on the Cantor space.
