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A note on minimal dynamical systems. (English) Zbl 1065.37008

Summary: Let \(G\) be a topological group acting continuously on an infinite compact space \(X\). Suppose the dynamical system \((X,G)\) is minimal, i.e., suppose that every point in \(X\) has a dense \(G\)-orbit. We show that \(X\) is coabsolute with a Cantor space if \(G\) is \(\omega\)-bounded. This generalizes a theorem of B. Balcar and A. Blaszcyk [Commentat. Math. Univ. Carol. 31, 7–11 (1990; Zbl 0697.54021)].

MSC:

37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
54H20 Topological dynamics (MSC2010)

Citations:

Zbl 0697.54021
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