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{Ind f, 0}: Then the set of regular values of f is residual in N.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 12, pp. 1634–1641, December, 2010.
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Eftekharinasab, K. Sard’s theorem for mappings between Fréchet manifolds. Ukr Math J 62, 1896–1905 (2011). https://doi.org/10.1007/s11253-011-0478-z
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DOI: https://doi.org/10.1007/s11253-011-0478-z