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On free actions, minimal flows, and a problem by Ellis. (English) Zbl 0911.54034
This is an important article. The author exhibits natural classes of Polish topological groups \(G\) such that every continuous action of \(G\) on a compact space has a fixed point, and observes that every group with this property provides a solution (in the negative) to a 1969 problem by Robert Ellis, as the Ellis semigroup \(E(U)\) of the universal minimal \(G\)-flow \(U\), being trivial, is not isomorphic with the greatest \(G\)-ambit. There are also many other interesting results.
Reviewer: T.S.Wu (Cleveland)

MSC:
54H20 Topological dynamics (MSC2010)
54E45 Compact (locally compact) metric spaces
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