Definable compactness in definably complete locally o-minimal structures
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916489495314432 |
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| author | Fujita, Masato |
| author_facet | Fujita, Masato |
| contents | We demonstrate that Andújar Guerrero, Thomas and Walsberg's results on definable compactness in o-minimal structures still hold true in definably complete locally o-minimal structures. As an application, we show that a definably simple definable topological group which is regular, Hausdorff and definably compact as a definable topological space is either discrete or definably connected. We also study the definable quotient of definable continuous actions by definably compact definable topological groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_01644 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Definable compactness in definably complete locally o-minimal structures Fujita, Masato Logic Primary 03C64, Secondary 54D30, 22C05, 54H11 We demonstrate that Andújar Guerrero, Thomas and Walsberg's results on definable compactness in o-minimal structures still hold true in definably complete locally o-minimal structures. As an application, we show that a definably simple definable topological group which is regular, Hausdorff and definably compact as a definable topological space is either discrete or definably connected. We also study the definable quotient of definable continuous actions by definably compact definable topological groups. |
| title | Definable compactness in definably complete locally o-minimal structures |
| topic | Logic Primary 03C64, Secondary 54D30, 22C05, 54H11 |
| url | https://arxiv.org/abs/2303.01644 |