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 $MC^k$ -Lipsc...
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| Date: | 2010 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2010
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2988 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509000005582848 |
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| author | Eftekharinasab, К. Ефтехарінасаб, К. |
| author_facet | Eftekharinasab, К. Ефтехарінасаб, К. |
| author_sort | Eftekharinasab, К. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T19:41:53Z |
| description | 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 $k > \max \{\text{Ind}\; f, 0\}$. Then the set of regular values of $f$ is residual in $N$. |
| first_indexed | 2026-03-24T02:34:08Z |
| format | Article |
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| id | umjimathkievua-article-2988 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:34:08Z |
| publishDate | 2010 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/21/50a80cec0878044ed34382a332f38b21.pdf |
| spelling | umjimathkievua-article-29882020-03-18T19:41:53Z Sard’s theorem for mappings between Fréchet manifolds Теорема Сарда для відображень між многовидами Фреше Eftekharinasab, К. Ефтехарінасаб, К. 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 $k > \max \{\text{Ind}\; f, 0\}$. Then the set of regular values of $f$ is residual in $N$. Доведено нескінченновимірну версію теореми Сарда для многовидів Фреше. Припустимо, що $M$ і відповідно $N$ — обмежені многовиди із сумісними метриками $d_M$ (відповідно $d_N$), які змодельовані на просторах Фреше $E$ (відповідно $F$) зі стандартними метриками. Нехай $f : M → N$ буде $MC^k$ - відображенням Ліпшиця-Фредгольма з $k > \max \{\text{Ind}\; f, 0\}$. Тоді множина регулярних значень $f$ є залишковою в $N$. Institute of Mathematics, NAS of Ukraine 2010-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/2988 Ukrains’kyi Matematychnyi Zhurnal; Vol. 62 No. 12 (2010); 1634–1641 Український математичний журнал; Том 62 № 12 (2010); 1634–1641 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/2988/2726 https://umj.imath.kiev.ua/index.php/umj/article/view/2988/2727 Copyright (c) 2010 Eftekharinasab К. |
| spellingShingle | Eftekharinasab, К. Ефтехарінасаб, К. Sard’s theorem for mappings between Fréchet manifolds |
| title | Sard’s theorem for mappings between Fréchet manifolds |
| title_alt | Теорема Сарда для відображень між многовидами Фреше |
| title_full | Sard’s theorem for mappings between Fréchet manifolds |
| title_fullStr | Sard’s theorem for mappings between Fréchet manifolds |
| title_full_unstemmed | Sard’s theorem for mappings between Fréchet manifolds |
| title_short | Sard’s theorem for mappings between Fréchet manifolds |
| title_sort | sard’s theorem for mappings between fréchet manifolds |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/2988 |
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