Intermediate values and inverse functions on non-Archimedean fields
type: Item
instance of: scholarly article
title: Intermediate values and inverse functions on non-Archimedean fields
zbMATH Open document ID: 0996.26020
DOI: 10.1155/S0161171202013030
author: Khodr Shamseddine
author: Martin Berz
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-12T00:00:00Z
full work available at URL: https://eudml.org/doc/49458
full work available at URL: S0161171202013030.html
review text: Summary: Continuity or even differentiability of a function on a closed interval of a non-Archimedean field are not sufficient for the function to assume all the intermediate values, a maximum, a minimum, or a unique primitive function on the interval. These problems are due to the total disconnectedness of the field in the order topology. In this paper, we show that differentiability (in the topological sense), together with some additional mild conditions, is indeed sufficient to guarantee that the function assumes all intermediate values and has a differentiable inverse function.
Mathematics Subject Classification ID: 26E30
Mathematics Subject Classification ID: 11D88
Mathematics Subject Classification ID: 12J25
zbMATH DE Number: 1779105
zbMATH Keywords: non-Archimedean field
zbMATH Keywords: indeterminate values
zbMATH Keywords: differentiability
zbMATH Keywords: differentiable inverse function
MaRDI profile type: Publication
OpenAlex ID: W2159762034
description: scientific article; zbMATH DE number 1779105