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.
@article{118954,
author = {Anzelm Iwanik},
title = {How restrictive is topological dynamics?},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {38},
year = {1997},
pages = {563-569},
zbl = {0938.54036},
mrnumber = {1485077},
language = {en},
url = {http://dml.mathdoc.fr/item/118954}
}
Iwanik, Anzelm. How restrictive is topological dynamics?. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 563-569. http://gdmltest.u-ga.fr/item/118954/
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