Un r\'esultat de connexit\'e pour les vari\'et\'es analytiques   p-adiques. Privil\`ege et noeth\'erianit\'e
  Let $k$ be a non-Archimedean field, $X$ a $k$-affinoid space and $f$ an analytic function over $X$. We precisely describe how the geometric connected components of the spaces $\{x \in X, |f(x)| \ge \varepsilon\}$ behave with regards to $\varepsilon$. We also obtain a result concerning privileged neighbourhoods and adapt a theorem from complex analytic geometry about Noetherianity for germs of analytic functions. 
J\'er\^ome Poineau