NTP2 topological structures
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917510834552832 |
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| author | Guerrero, Pablo Andújar |
| author_facet | Guerrero, Pablo Andújar |
| contents | A subset of a topological space is constructible if it is a finite Boolean combination of closed sets. We prove that every NTP$_2$ expansion of $(\mathbb{R},<,+)$ by constructible sets defines only constructible sets, and that definable functions are generically piecewise continuous. The result also holds for all NTP$_2$ expansions of $(\mathbb{Q}_p,+,\cdot)$, and all NTP$_2$ definably complete expansions of ordered groups. In the latter case, the structure is generically locally o-minimal, has definable choice, and carries a well-behaved notion of naive topological dimension. For NIP uniform topological structures, constructibility of definable sets is preserved in the Shelah expansion. We classify strong expansions of $(\mathbb{R},<,+)$ by constructible sets, and obtain results on NTP$_2$ d-minimal structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24522 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | NTP2 topological structures Guerrero, Pablo Andújar Logic 03C45, 03C64 (Primary), 54H05 (Secondary) A subset of a topological space is constructible if it is a finite Boolean combination of closed sets. We prove that every NTP$_2$ expansion of $(\mathbb{R},<,+)$ by constructible sets defines only constructible sets, and that definable functions are generically piecewise continuous. The result also holds for all NTP$_2$ expansions of $(\mathbb{Q}_p,+,\cdot)$, and all NTP$_2$ definably complete expansions of ordered groups. In the latter case, the structure is generically locally o-minimal, has definable choice, and carries a well-behaved notion of naive topological dimension. For NIP uniform topological structures, constructibility of definable sets is preserved in the Shelah expansion. We classify strong expansions of $(\mathbb{R},<,+)$ by constructible sets, and obtain results on NTP$_2$ d-minimal structures. |
| title | NTP2 topological structures |
| topic | Logic 03C45, 03C64 (Primary), 54H05 (Secondary) |
| url | https://arxiv.org/abs/2604.24522 |