Fréchet流形之间映射的Sard定理
Sard's theorem for mappings between Fréchet manifolds
摘要：
本文证明了Fréchet流形上的Sard定理的一个无限维版本。设$ M $和$ N $是有界Fréchet流形，使得它们的模型Fréchet空间的拓扑由具有绝对凸球的度量定义.设$ f: M \rightarrow N $是一个具有$ k > \max \lbrace {\Ind f,0} \rbrace $的$ MC^k$ -Lipschitz-Fredholm映射.则$ f $的正则值集在$ N $中是残差。
英文摘要：
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 \rightarrow N $ be an $ MC^k$-Lipschitz-Fredholm map with $ k > \max \lbrace {\Ind f,0} \rbrace $. Then the set of regular values of $ f $ is residual in $ N $.
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