On analytic functions in an ordered field with an infinite rank valuation

Abstract

Let K be the scalar field of the first orthomodular (or Form Hilbert) space, described by H. Keller in 1980. It has a non-Archimedean order, an infinite rank valuation compatible with the order as well as an explicitly defined ultrametric, all of which induce the same topology. We study analytic functions defined on valued field K, and we will establish an invertibility local theorem for these functions as an application of Banach fixed point theorem.