Strictly injective analytic elements on an infraconnected affinoid set

In this paper, we will prove that every injective analytic element on an infraconnected affinoid set is an infinite product of homographic functions where one of these dominates the others. This problem is suggested by A. Escassut and M.-C. Sarmant and still open. The key point of the proof is to analyze the Mittag-Leffler series of strictly injective analytic elements. For this purpose, some technical claims are needed and proved by elementary [Formula: see text]-adic analysis.