Transversality and Lipschitz-Fredholm maps
We study transversality for Lipschitz-Fredholm maps in the context of bounded Fréchet manifolds. We show that the set of all Lipschitz-Fredholm maps of a fixed index between Fréchet spaces has the transverse stability property. We give a straightforward extension of the Smale transversality theore...
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| Date: | 2015 |
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| Keywords: | keywords |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/133 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | We study transversality for Lipschitz-Fredholm maps in the context of bounded Fréchet manifolds. We show that the set of all Lipschitz-Fredholm maps of a fixed index between Fréchet spaces has the transverse stability property. We give a straightforward extension of the Smale transversality theorem by using the generalized Sard’s theorem for this category of man-ifolds. We also provide an answer to the well known problem concerning the existence of a submanifold structure on the preimage of a transversal submanifold. |
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