{"paper":{"title":"On regulous and regular images of Euclidean spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Carlos Ueno, Goulwen Fichou (IRMAR), Jos\\'e Fernando (UCM), Ronan Quarez (IRMAR)","submitted_at":"2017-10-19T12:49:29Z","abstract_excerpt":"In this work we compare the semialgebraic subsets that are images of regulous maps with those that are images of regular maps. Recall that a map f : R n $\\rightarrow$ R m is regulous if it is a rational map that admits a continuous extension to R n. In case the set of (real) poles of f is empty we say that it is regular map. We prove that if S $\\subset$ R m is the image of a regulous map f : R n $\\rightarrow$ R m , there exists a dense semialgebraic subset T $\\subset$ S and a regular map g : R n $\\rightarrow$ R m such that g(R n) = T. In case dim(S) = n, we may assume that the difference S \\ T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08276","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"}