Sard’s theorem for mappings between Fréchet manifolds - Eftekharinasab К. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
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 > {Ind f, 0}. Then the set of regular values of f is residual in N.