{"paper":{"title":"On the set of points at infinity of a polynomial image 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":"2012-12-08T16:24:40Z","abstract_excerpt":"In this work we prove that the set of points at infinity $S_\\infty:={\\rm Cl}_{{\\mathbb R}{\\mathbb P}^m}(S)\\cap\\mathsf{H}_\\infty$ of a semialgebraic set $S\\subset{\\mathbb R}^m$ which is the image of a polynomial map $f:{\\mathbb R}^n\\to{\\mathbb R}^m$ is connected. This result is no further true in general if $f$ is a regular map, although it still works for a large family of regular maps that we call quasi-polynomial maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1811","kind":"arxiv","version":3},"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"}