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Keywords:
abstract dynamical system; pointwise periodic system; symbolic dynamics; $\bold Z^2$-action
abstract dynamical system; pointwise periodic system; symbolic dynamics; $\bold Z^2$-action
Summary:
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 ${\bold Z}^2$-actions without periodic points.
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