Abstract
We prove that, whenever G is a Polish group with metrizable universal minimal flow M(G), there exists a comeagre orbit in M(G). It then follows that there exists an extremely amenable, closed, co-precompact subgroup G * of G such that \({M(G) = \widehat{G/G^*}}\).
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Ben Yaacov, I., Melleray, J. & Tsankov, T. Metrizable universal minimal flows of Polish groups have a comeagre orbit. Geom. Funct. Anal. 27, 67–77 (2017). https://doi.org/10.1007/s00039-017-0398-7
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DOI: https://doi.org/10.1007/s00039-017-0398-7