Let $G$ be a polish group, $H$ be an open subgroup of $G$ and $X$ be any metric space on which $H$ act continuously. Let $f:G\longrightarrow X$ such that $\forall h\in H$ and $\forall g\in G$, $f(gh)=h^{-1}f(g)$. I want to show that $f$ is continuous. Thank for any help
polish groups and open subgroups
2
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group-theory