Sard's theorem for mappings between Fréchet manifolds

Details Sard's theorem for mappings between Fréchet manifolds Sard's theorem for mappings between Fréchet manifolds

2010-04-27

arxiv.org/abs/1004.4900v4

Ukrainian mathematical Journal, vol 64, no 12, pp. 1634-- 1641 (2010)

Mathematics

Functional Analysis

Scientific paper

In this paper we prove an infinite-dimensional version of Sard's theorem for Fr\'{e}chet manifolds. Let $ M $ resp. $ N $ be bounded Fr\'echet manifolds with compatible metrics $ d_M $ resp. $ d_N$ modelled on Fr\'echet spaces $ E$ resp. $F $ with standard metrics. Let $ f: M \to 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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