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

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 $\mathrm{\mid }f\mathrm{\mid }\le r\mathrm{\mid }g\mathrm{\mid }$, 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 $\sqrt{\rho (A)}$.