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Polish groups with metrizable universal minimal flows

Abstract : We prove that if the universalminimal flow of a Polish group G is metrizable and contains a comeagre orbit O, then it is isomorphic to the completion of the homogeneous space G/O and show how this result translates naturally in terms of structural Ramsey theory. We also investigate universal minimal proximal flows and describe concrete representations of them in a number of examples.
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Submitted on : Thursday, April 24, 2014 - 10:48:02 PM
Last modification on : Wednesday, February 9, 2022 - 11:02:03 AM
Long-term archiving on: : Thursday, July 24, 2014 - 11:57:04 AM

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Julien Melleray, Lionel Nguyen van Thé, Todor Tsankov. Polish groups with metrizable universal minimal flows. International Mathematics Research Notices, Oxford University Press (OUP), 2015, 2016 (5), pp.1285-1307. ⟨10.1093/imrn/rnv171⟩. ⟨hal-00983248⟩

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