The implicit function theorem in a non-Archimedean setting
type: Item
instance of: scholarly article
title: The implicit function theorem in a non-Archimedean setting
zbMATH Open document ID: 1217.26063
DOI: 10.1016/S0019-3577(09)80028-1
author: Khodr Shamseddine
author: Trevor Rempel
author: Todd Sierens
published in: Indagationes Mathematicae. New Series
publication date: 2011-03-31T00:00:00Z
review text: Let \(\mathcal N\) be a non-Archimedean field extension of the field \(\mathbb R\) of real numbers. It is assumed that \(\mathcal N\) is real closed and Cauchy complete in the topology induced by the order. The authors study locally uniformly differentiable functions from \(\mathcal N^n\) to \(\mathcal N^m\) and prove the inverse function theorem for functions \(\mathcal N^n\to \mathcal N^n\) and the implicit function theorem for functions \(\mathcal N^n\to \mathcal N^m\), \(m<n\).
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 26E30
Mathematics Subject Classification ID: 12J25
Mathematics Subject Classification ID: 26B10
zbMATH DE Number: 5872501
zbMATH Keywords: non-Archimedean field
zbMATH Keywords: real closed field
zbMATH Keywords: inverse function theorem
zbMATH Keywords: implicit function theorem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5872501