Todorc̆ević’ trichotomy and a hierarchy in the class of tame dynamical systems

Todorc̆ević’ trichotomy in the class of separable Rosenthal compacta induces a hierarchy tame (compact, metrizable) dynamical systems ( X , T stretchy="false">) (X,T) according to topological properties their enveloping semigroups alttext="upper E left-parenthesis E encoding="application/x-tex">E(X) . More precisely, we define classes T mathvariant="normal">a mathvariant="normal">m mathvariant="normal">e 2 ⊂ mathvariant="bold">1 encoding="application/x-tex">\begin{equation*} \mathrm {Tame}_\mathbf {2} \subset {1} {Tame}, \end{equation*} where 1"> encoding="application/x-tex">\mathrm {1} is proper subclass with first countable , and 2"> {2} its consisting hereditarily We study some general these exhibit many examples illustrate properties.