{"paper":{"title":"On complements of convex polyhedra as polynomial and regular images of $\\R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Carlos Ueno, Jos\\'e F. Fernando","submitted_at":"2012-12-08T16:32:48Z","abstract_excerpt":"In this work we prove constructively that the complement $\\R^n\\setminus\\pol$ of a convex polyhedron $\\pol\\subset\\R^n$ and the complement $\\R^n\\setminus\\Int(\\pol)$ of its interior are regular images of $\\R^n$. If $\\pol$ is moreover bounded, we can assure that $\\R^n\\setminus\\pol$ and $\\R^n\\setminus\\Int(\\pol)$ are also polynomial images of $\\R^n$. The construction of such regular and polynomial maps is done by double induction on the number of \\em facets \\em (faces of maximal dimension) and the dimension of $\\pol$; the careful placing (\\em first \\em and \\em second trimming positions\\em) of the in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1813","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"}