Sur les composantes connexes d'une famille d'espaces analytiques p-adiques

Abstract

Let $X=\mathcal{M}(A)$ be an affinoid space and let $f,g \in A$. We study the sets of connected components of the spaces defined by an inequality of the form $|f|\le r|g|$, with $r\ge 0$. We prove that there exists a finite partition of $\mathbb{R}_+$ into intervals where those sets are canonically in bijection and that the bounds of those intervals belong to $\sqrt{\rho(A)}$.