Metrizable universal minimal flows of Polish groups have a comeagre orbit
Résumé
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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