Intermediate Values and Inverse Functions on Non-Archimedean Fields
AbstractContinuity 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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