Sard’s theorem for mappings between Fréchet manifolds

Abstract

We prove an infinite-dimensional version of Sard’s theorem for Fréchet manifolds. Let $M$ (respectively, $N$) be a bounded Fréchet manifold with compatible metric $d_M$ (respectively, $d_N$ ) modeled on Fréchet spaces $E$ (respectively, $F$) with standard metrics. Let $f : M → N$ be an $MC^k$ -Lipschitz–Fredholm map with $k > \max \{\text{Ind}\; f, 0\}$. Then the set of regular values of $f$ is residual in $N$.