Extension of Lipschitz maps definable in Hensel minimal structures
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914413797179392 |
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| author | Nowak, Krzysztof Jan |
| author_facet | Nowak, Krzysztof Jan |
| contents | In this paper, we establish a theorem on extension of Lipschitz maps $f$ definable in Hensel minimal fields $K$. This may be regarded as a definable, non-Archimedean, non-locally compact version of Kirszbraun's extension theorem. We proceed with double induction with respect to the dimensions of the ambient space and of the domain of $f$. To this end, we introduce the concept of a definable open cell package with a skeleton which, along with the concept of a risometry, plays a key role in our induction procedure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2204_05900 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Extension of Lipschitz maps definable in Hensel minimal structures Nowak, Krzysztof Jan Logic Algebraic Geometry 03C65, 12J25, 51F30, 32B20, 32P05, 03C98 In this paper, we establish a theorem on extension of Lipschitz maps $f$ definable in Hensel minimal fields $K$. This may be regarded as a definable, non-Archimedean, non-locally compact version of Kirszbraun's extension theorem. We proceed with double induction with respect to the dimensions of the ambient space and of the domain of $f$. To this end, we introduce the concept of a definable open cell package with a skeleton which, along with the concept of a risometry, plays a key role in our induction procedure. |
| title | Extension of Lipschitz maps definable in Hensel minimal structures |
| topic | Logic Algebraic Geometry 03C65, 12J25, 51F30, 32B20, 32P05, 03C98 |
| url | https://arxiv.org/abs/2204.05900 |