Morse functions definable in d-minimal structures
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909473187037184 |
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| author | Fujita, Masato |
| author_facet | Fujita, Masato |
| contents | Fix a d-minimal expansion of an ordered field. We consider the space $\mathcal D^p(M)$ of definable $\mathcal C^p$ functions defined on a definable $\mathcal C^p$ submanifold $M$ equipped with definable $\mathcal C^p$ topology. The set of definable $\mathcal C^p$ Morse functions is dense in $\mathcal D^p(M)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01082 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Morse functions definable in d-minimal structures Fujita, Masato Logic 03C64, 57R35 Fix a d-minimal expansion of an ordered field. We consider the space $\mathcal D^p(M)$ of definable $\mathcal C^p$ functions defined on a definable $\mathcal C^p$ submanifold $M$ equipped with definable $\mathcal C^p$ topology. The set of definable $\mathcal C^p$ Morse functions is dense in $\mathcal D^p(M)$. |
| title | Morse functions definable in d-minimal structures |
| topic | Logic 03C64, 57R35 |
| url | https://arxiv.org/abs/2502.01082 |