Let $\Omega$ be a non-archimedean complete field, $n\in\mathbb N$ and $f:\Omega^n\to\Omega^n$ be an injective analytic map. Is the application $f$ open?
In the complex case, this is a consequence of a Remmert theorem, but in the non-archimedean case, I do not know.
Thanks in advance for any answer.