A remark on $\mathscr{C}^\infty$ definable equivalence
| Autor: | Valette, Anna, Valette, Guillaume |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Annales Polonici Mathematici vol. 131.1 (2023), 79-84 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4064/ap230321-10-8 |
| Popis: | We establish that if a submanifold $M$ of $\mathbb{R}^n$ is definable in some o-minimal structure then any definable submanifold $N\subset \mathbb{R}^n$ which is $\mathscr{C}^\infty$ diffeomorphic to $M$, with a diffeomorphism $h:N\to M$ that is sufficiently close to the identity, must be $\mathscr{C}^\infty$ definably diffeomorphic to $M$. The definable diffeomorphism between $N$ and $M$ is then provided by a tubular neighborhood of $M$. Comment: Final version |
| Databáze: | arXiv |
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