Definable $\mathcal C^r$ structures on definable topological groups in d-minimal structures
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917730698919936 |
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| author | Fujita, Masato |
| author_facet | Fujita, Masato |
| contents | Definable topological groups whose topologies are affine have definable $\mathcal C^r$ structures in d-minimal expansions of ordered fields, where $r$ is a positive integer. We prove this fact using a new notion called partition degree of a definable set. Basic properties of partition degree are also studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15647 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Definable $\mathcal C^r$ structures on definable topological groups in d-minimal structures Fujita, Masato Logic Primary 03C64, Secondary 54H11 Definable topological groups whose topologies are affine have definable $\mathcal C^r$ structures in d-minimal expansions of ordered fields, where $r$ is a positive integer. We prove this fact using a new notion called partition degree of a definable set. Basic properties of partition degree are also studied. |
| title | Definable $\mathcal C^r$ structures on definable topological groups in d-minimal structures |
| topic | Logic Primary 03C64, Secondary 54H11 |
| url | https://arxiv.org/abs/2404.15647 |