{"paper":{"title":"Differentiable approximation of continuous semialgebraic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jos\\'e F. Fernando, Riccardo Ghiloni","submitted_at":"2018-05-09T13:43:21Z","abstract_excerpt":"In this work we approach the problem of approximating uniformly continuous semialgebraic maps $f:S\\to T$ from a compact semialgebraic set $S$ to an arbitrary semialgebraic set $T$ by semialgebraic maps $g:S\\to T$ that are differentiable of class~${\\mathcal C}^\\nu$ for a fixed integer $\\nu\\geq1$. As the reader can expect, the difficulty arises mainly when one tries to keep the same target space after approximation. For $\\nu=1$ we give a complete affirmative solution to the problem: such a uniform approximation is always possible. For $\\nu \\geq 2$ we obtain density results in the two following r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03520","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"}