Topological dynamics of automorphism groups, ultrafilter combinatorics, and the Generic Point Problem
Topological dynamics of automorphism groups, ultrafilter combinatorics, and the Generic Point Problem
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自同构群的拓扑动力学、超滤组合学和泛型点问题
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发表时间：
2015
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通讯作者：
Andy Zucker
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作者：
Andy Zucker
对S∞的闭子群G，给出了泛极小流M（G）可度量化的精确组合刻划.特别地，每个这样的实例都适合于[KPT]和[NVT]中发展的可度量流的框架;因此，每个具有可度量泛极小流的G都具有一般点性质，即每个极小G-流都有一个其轨道是comeager的点。这解决了[AKL]中提出的S∞闭子群的通有点问题。
For G a closed subgroup of S∞, we provide a precise combinatorial characterization of when the universal minimal flow M(G) is metrizable. In particular, each such instance fits into the framework of metrizable flows developed in [KPT] and [NVT]; as a consequence, each G with metrizable universal minimal flow has the generic point property, i.e. every minimal G-flow has a point whose orbit is comeager. This solves the Generic Point Problem raised in [AKL] for closed subgroups of S∞.