{"paper":{"title":"Approximation of maps from algebraic polyhedra to real algebraic varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Marcin Bilski, Wojciech Kucharz","submitted_at":"2024-10-30T20:56:04Z","abstract_excerpt":"Given a finite simplicial complex $\\mathcal{K}$ in $\\mathbb{R}^n$ and a real algebraic variety $Y,$ by a $\\mathcal{K}$-regular map $|\\mathcal{K}|\\rightarrow Y$ we mean a continuous map whose restriction to every simplex in $\\mathcal{K}$ is a regular map. A simplified version of our main result says that if $Y$ is a uniformly retract rational variety and if $k, l$ are integers satisfying $0\\leq l\\leq k,$ then every $\\mathcal{C}^l$ map $|\\mathcal{K}|\\rightarrow Y$ can be approximated in the $\\mathcal{C}^l$ topology by $\\mathcal{K}$-regular maps of class $\\mathcal{C}^k.$ By definition, $Y$ is uni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.23457","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.23457/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}