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Title: Intermediate values and inverse functions on non-Archimedean fields

Abstract

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.

Authors:
 [1];  [2]
  1. Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
  2. Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1197847
Grant/Contract Number:  
FG02-95ER40931
Resource Type:
Published Article
Journal Name:
International Journal of Mathematics and Mathematical Sciences
Additional Journal Information:
Journal Name: International Journal of Mathematics and Mathematical Sciences Journal Volume: 30 Journal Issue: 3; Journal ID: ISSN 0161-1712
Publisher:
Hindawi Publishing Corporation
Country of Publication:
Country unknown/Code not available
Language:
English

Citation Formats

Shamseddine, Khodr, and Berz, Martin. Intermediate values and inverse functions on non-Archimedean fields. Country unknown/Code not available: N. p., 2002. Web. doi:10.1155/S0161171202013030.
Shamseddine, Khodr, & Berz, Martin. Intermediate values and inverse functions on non-Archimedean fields. Country unknown/Code not available. doi:10.1155/S0161171202013030.
Shamseddine, Khodr, and Berz, Martin. Tue . "Intermediate values and inverse functions on non-Archimedean fields". Country unknown/Code not available. doi:10.1155/S0161171202013030.
@article{osti_1197847,
title = {Intermediate values and inverse functions on non-Archimedean fields},
author = {Shamseddine, Khodr and Berz, Martin},
abstractNote = {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.},
doi = {10.1155/S0161171202013030},
journal = {International Journal of Mathematics and Mathematical Sciences},
number = 3,
volume = 30,
place = {Country unknown/Code not available},
year = {2002},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1155/S0161171202013030

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