Definable compactness in o-minimal structures
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918002306318336 |
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| author | Guerrero, Pablo Andújar |
| author_facet | Guerrero, Pablo Andújar |
| contents | We characterize the notion of definable compactness for topological spaces definable in o-minimal structures, answering questions of Peterzil and Steinhorn (1999) and Johnson (2018). Specifically, we prove the equivalence of various definitions of definable compactness in the literature, including those in terms of definable curves, definable types, and definable downward directed families of closed sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07112 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Definable compactness in o-minimal structures Guerrero, Pablo Andújar Logic General Topology 03C64 (Primary), 54A05, 54D30 (Secondary) We characterize the notion of definable compactness for topological spaces definable in o-minimal structures, answering questions of Peterzil and Steinhorn (1999) and Johnson (2018). Specifically, we prove the equivalence of various definitions of definable compactness in the literature, including those in terms of definable curves, definable types, and definable downward directed families of closed sets. |
| title | Definable compactness in o-minimal structures |
| topic | Logic General Topology 03C64 (Primary), 54A05, 54D30 (Secondary) |
| url | https://arxiv.org/abs/2405.07112 |