On locally uniformly differentiable functions on a complete non-Archimedean ordered field extension of the real numbers
type: Item
instance of: scholarly article
title: On locally uniformly differentiable functions on a complete non-Archimedean ordered field extension of the real numbers
zbMATH Open document ID: 1242.26042
DOI: 10.5402/2012/387053
author: Khodr Shamseddine
author: Todd Sierens
published in: ISRN Mathematical Analysis
publication date: 2012-06-26T00:00:00Z
review text: Summary: We study the properties of locally uniformly differentiable functions on \(\mathcal N\), a non-Archimedean field extension of the real numbers that is real closed and Cauchy complete in the topology induced by the order. In particular, we show that locally uniformly differentiable functions are \(C^1\), they include all polynomial functions, and they are closed under addition, multiplication, and composition. Then we formulate and prove a version of the inverse function theorem as well as a local intermediate value theorem for these functions.
Mathematics Subject Classification ID: 26E30
zbMATH DE Number: 6049785
zbMATH Keywords: non-Archimedean field extension
zbMATH Keywords: locally uniformly differentiable functions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/387053
OpenAlex ID: W2025974488
Wikidata QID: Q58690651
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description: scientific article; zbMATH DE number 6049785