{"paper":{"title":"A definable, p-adic analogue of Kirszbraun's Theorem on extensions of Lipschitz maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.AG","authors_text":"Florent Martin, Raf Cluckers","submitted_at":"2015-02-10T18:49:23Z","abstract_excerpt":"A direct application of Zorn's Lemma gives that every Lipschitz map $f:X\\subset \\mathbb{Q}_p^n\\to \\mathbb{Q}_p^\\ell$ has an extension to a Lipschitz map $\\widetilde f: \\mathbb{Q}_p^n\\to \\mathbb{Q}_p^\\ell$. This is analogous, but more easy, to Kirszbraun's Theorem about the existence of Lipschitz extensions of Lipschitz maps $S\\subset \\mathbb{R}^n\\to \\mathbb{R}^\\ell$. Recently, Fischer and Aschenbrenner obtained a definable version of Kirszbraun's Theorem. In the present paper, we prove in the $p$-adic context that $\\widetilde f$ can be taken definable when $f$ is definable, where definable mea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03036","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}