Sard's theorem for mappings between Fréchet manifolds

Abstract

In this paper we prove an infinite-dimensional version of Sard's theorem for Fréchet manifolds. Let $M$ and $N$ be bounded Fréchet manifolds such that the topologies of their model Fréchet spaces are defined by metrics with absolutely convex balls. Let $f:M\to N$ be an $M{C}^k$-Lipschitz-Fredholm map with $ k > \max \lbrace {\Ind f,0} \rbrace $. Then the set of regular values of $f$ is residual in $N$.

Cited by in corpus (3)

• Geometry of Bounded Frechet Manifolds
• On local definability of holomorphic functions
• Some applications of transversality for infinite dimensional manifolds