Sard’s theorem for mappings between Fréchet manifolds
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...
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| Date: | 2010 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2010
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| Series: | Український математичний журнал |
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/166299 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Sard’s theorem for mappings between Fréchet manifolds / K. Eftekharinasab // Український математичний журнал. — 2010. — Т. 62, № 12. — С. 1634–1641. — Бібліогр.: 5 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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