Geodesic
How restrictive is topological dynamics?
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 3, pp. 563-569.

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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 ${\bold Z}^2$-actions without periodic points.
Classification : 54H20
Keywords: abstract dynamical system; pointwise periodic system; symbolic dynamics; $\bold Z^2$-action 
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Iwanik, A. How restrictive is topological dynamics?. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 3, pp. 563-569. http://geodesic.mathdoc.fr/item/CMUC_1997__38_3_a12/