Intermediate values and inverse functions on non-Archimedean fields

Shamseddine, Khodr; Berz, Martin

doi:10.1155/S0161171202013030

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

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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:

Shamseddine, Khodr ^[1]; Berz, Martin ^[2]

Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA

Publication Date:: Tue Jan 01 00:00:00 EST 2002

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.

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                    Shamseddine, Khodr, & Berz, Martin. Intermediate values and inverse functions on non-Archimedean fields.  Country unknown/Code not available.  https://doi.org/10.1155/S0161171202013030

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                    Shamseddine, Khodr, and Berz, Martin. Tue .  
"Intermediate values and inverse functions on non-Archimedean fields".  Country unknown/Code not available.  https://doi.org/10.1155/S0161171202013030.

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@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         = {Tue Jan 01 00:00:00 EST 2002},

  month        = {Tue Jan 01 00:00:00 EST 2002}

}

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