Topological Dynamics of Closed Subgroups of $S_\infty$

Andy Zucker

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arXiv · 1404.5057

Topological Dynamics of Closed Subgroups of $S_\infty$

Andy Zucker

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Abstract

For $G$ a closed subgroup of $S_{\infty}$, we provide an explicit characterization of the greatest $G$-ambit. Using this, we provide a precise characterization of when $G$ has metrizable universal minimal flow. In particular, each such instance fits into the framework of metrizable flows developed by Kechris-Pestov-Todorcevic and Nguyen Van Thé; as a consequence, each $G$ with metrizable universal minimal flow has the generic point property.

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BibTeX RIS

Andy Zucker. 2014-05-07. Topological Dynamics of Closed Subgroups of $S_\infty$. https://arxiv.org/abs/1404.5057

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