论文标题
波兰群体以外的拓扑动态
Topological dynamics beyond Polish groups
论文作者
论文摘要
当$ g $是波兰人的群体时，通用最小流量的衡量性被证明是$ g $的拓扑动力学复杂性的强大分界线。我们介绍了一类小组，即CAP组，该组对所有拓扑组都提供了该分界线的整洁概括。我们证明了此类的许多特征，具有截然不同的口味，并使用这些特征来证明CAP组的类别具有许多不错的封闭属性。作为一种具体的应用，我们根据Gheysens最近的工作基础，计算了几个分散拓扑空间的同构群体的普遍流动。
When $G$ is a Polish group, metrizability of the universal minimal flow has been shown to be a robust dividing line in the complexity of the topological dynamics of $G$. We introduce a class of groups, the CAP groups, which provides a neat generalization of this dividing line to all topological groups. We prove a number of characterizations of this class, having very different flavors, and use these to prove that the class of CAP groups enjoys a number of nice closure properties. As a concrete application, we compute the universal minimal flow of the homeomorphism groups of several scattered topological spaces, building on recent work of Gheysens.
