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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 assume all intermediate values and have a differentiable inverse function.

K. Shamseddine, M. Berz, International Journal of Mathematics and Mathematical Sciences 30(3) (2002) 165-176

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