I have a question about the strong G-topology of an affinoid variety. In particular let $X=Sp(A)$ be an affinoid variety and we consider analytic functions $f_1,...,f_m\in A$ on X, having no commom zero on X. I am wondering if the sets
$U_i=\lbrace x\in X \mid f_j(x)<f_i(x) \ \textit{for all} \ j<i \ \textit{and} \ f_j(x)\leq f_i(x) \ \textit{for all} \ \ j\geq i\rbrace$
are admissible open with respect to the strong G-topology. I think one can apply the same arguments as presented in Bosch's book https://link.springer.com/book/9783540125464 in chapter 9.1.4. Proposition 5, but I am not so sure. Maybe this is obvious or totally rubish, but unfortunately I am totally new to the subject and have no intution about auch things.
Moreover if the $U_i$ are admissible, is it than also true, that the covering $\lbrace U_i\rbrace$ is also an admissible covering of $X$? That the sets $U_i$ cover $X$ is obvious, but is it an admissible covering?
Many thanks if someone could help me out.