{"paper":{"title":"On complements of convex polyhedra as polynomial images of ${\\mathbb R}^n$","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":"2014-12-16T18:15:20Z","abstract_excerpt":"In this work we prove constructively that the complement ${\\mathbb R}^n\\setminus{\\mathcal K}$ of an $n$-dimensional unbounded convex polyhedron ${\\mathcal K}\\subset{\\mathbb R}^n$ and the complement ${\\mathbb R}^n\\setminus{\\rm Int}({\\mathcal K})$ of its interior are polynomial images of ${\\mathbb R}^n$ whenever ${\\mathcal K}$ does not disconnect ${\\mathbb R}^n$. The compact case and the case of convex polyhedra of small dimension were approached by the authors in previous works. Consequently, the results of this article provide a full answer to the representation as polynomial images of Euclide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5107","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":""},"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"}