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arXiv · 2011.04376

Todorcevi\'{c}' trichotomy and a hierarchy in the class of tame dynamical systems

Eli Glasner·Michael Megrelishvili
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Abstract

Todorcevi\'{c}' trichotomy in the class of separable Rosenthal compacta induces a hierarchy in the class of tame (compact, metrizable) dynamical systems $(X,T)$ according to the topological properties of their enveloping semigroups $E(X)$. More precisely, we define the classes $\mathrm{Tame}_\mathbf{2} \subset \mathrm{Tame}_\mathbf{1} \subset \mathrm{Tame},$ where $\mathrm{Tame}_\mathbf{1}$ is the proper subclass of tame systems with first countable $E(X)$, and $\mathrm{Tame}_\mathbf{2}$ is its proper subclass consisting of systems with hereditarily separable $E(X)$. We study some general properties of these classes and exhibit many examples to illustrate these properties.

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Eli Glasner, Michael Megrelishvili. 2020-11-09. Todorcevi\'{c}' trichotomy and a hierarchy in the class of tame dynamical systems. https://arxiv.org/abs/2011.04376

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