Overconvergent subanalytic subsets in the framework of Berkovich spaces (Q344466)

The geometry of overconvergent analytic maps and overconvergent subanalytic subsets of a \(k\)-affinoid space \(X\) (\(k\) is a non-Archimedean field) was developed by \textit{H. Schoutens} [Compos. Math. 94, No. 3, 269--295 (1994; Zbl 0867.32012)]. The overconvergent subanalytic subsets are the images along the projection \(X\times \mathbb B^n\to X\) (\(\mathbb B\) is a closed disk of radius 1) of subsets defined by inequalities between functions on \(X\times \mathbb B^n\), which are overconvergent in the variables of \(\mathbb B^n\).NEWLINENEWLINEThe author studies the behavior of such subsets in the Berkovich topology. Some erroneous statements from the above paper by \textit{H. Schoutens} and his paper \textit{H. Schoutens} [J. Algebra 170, No. 1, 266--276 (1994; Zbl 0826.14014)] are corrected using the techniques of Berkovich spaces. For the case where \(\dim X=2\), a simpler characterization of overconvergent subanalytic subsets is given.