Some applications of transversality for infinite dimensional manifolds

Abstract

We present some transversality results for a category of Fréchet manifolds, the so-called $M{C}^k$-Fréchet manifolds. In this context, we apply the obtained transversality results to construct the degree of nonlinear Fredholm mappings by virtue of which we prove a rank theorem, an invariance of domain theorem and a Bursuk-Ulam type theorem.