An infinite version of the Pólya enumeration theorem.

Bekes, Robert A.

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Aleksander Całka (1984)

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How restrictive is topological dynamics?

Anzelm Iwanik (1997)

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Let $T$ be a permutation of an abstract set $X$ . In ZFC, we find a necessary and sufficient condition it terms of cardinalities of the $T$ -orbits that allows us to topologize $(X, T)$ as a topological dynamical system on a compact Hausdorff space. This extends an early result of H. de Vries concerning compact metric dynamical systems. An analogous result is obtained for $𝐙^{2}$ -actions without periodic points.