Abstract
In this paper, the inverse function theorem and the implicit function theorem in a non-Archimedean setting will be discussed. We denote by N any non-Archimedean field extension of the real numbers that is real closed and Cauchy complete in the topology induced by the order; and we study the properties of locally uniformly differentiable functions from N n to N m . Then we use that concept of local uniform differentiability to formulate and prove the inverse function theorem for functions from N n to N n and the implicit function theorem for functions from N n to N m with m< n.
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