The implicit function theorem in a non-Archimedean setting
Let \(\mathcal N\) be a non-Archimedean field extension of the field \(\mathbb R\) of real numbers. It is assumed that \(\mathcal N\) is real closed and Cauchy complete in the topology induced by the order. The authors study locally uniformly differentiable functions from \(\mathcal N^n\) to \(\mathcal N^m\) and prove the inverse function theorem for functions \(\mathcal N^n\to \mathcal N^n\) and the implicit function theorem for functions \(\mathcal N^n\to \mathcal N^m\), \(m<n\).
scientific article; zbMATH DE number 5872501
scientific article