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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.14222 |
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| _version_ | 1866910403067379712 |
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| author | Fujita, Masato |
| author_facet | Fujita, Masato |
| contents | Thamrongthanyalak demonstrated a definable version of Michael's selection theorem in d-minimal expansions of the real field. We generalize this result to the case in which the structures are d-minimal expansions of ordered fields $\mathcal F=(F,<,+,\cdot,0,1,\ldots)$. We also show that we can choose a definable continuous selection $f$ of a lower semi-continuous map $T:E \rightrightarrows F$ so that $f(x)$ is contained in the interior of $T(x)$ when the interior is not empty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14222 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Michael's selection theorem in general d-minimal structures Fujita, Masato Logic Thamrongthanyalak demonstrated a definable version of Michael's selection theorem in d-minimal expansions of the real field. We generalize this result to the case in which the structures are d-minimal expansions of ordered fields $\mathcal F=(F,<,+,\cdot,0,1,\ldots)$. We also show that we can choose a definable continuous selection $f$ of a lower semi-continuous map $T:E \rightrightarrows F$ so that $f(x)$ is contained in the interior of $T(x)$ when the interior is not empty. |
| title | Michael's selection theorem in general d-minimal structures |
| topic | Logic |
| url | https://arxiv.org/abs/2402.14222 |