The implicit function theorem in a non-Archimedean setting *

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 Nn to Nm. Then we use that concept of local uniform differentiability to formulate and prove the inverse function theorem for functions from Nn to Nn and the implicit function theorem for functions from Nn to Nm with m