{"paper":{"title":"On Nash images of Euclidean spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jos\\'e F. Fernando","submitted_at":"2015-03-19T10:59:46Z","abstract_excerpt":"In this work we characterize the subsets of ${\\mathbb R}^n$ that are images of Nash maps $f:{\\mathbb R}^m\\to{\\mathbb R}^n$. We prove Shiota's conjecture and show that a subset ${\\mathcal S}\\subset{\\mathbb R}^n$ is the image of a Nash map $f:{\\mathbb R}^m\\to{\\mathbb R}^n$ if and only if ${\\mathcal S}$ is semialgebraic, pure dimensional of dimension $d\\leq m$ and there exists an analytic path $\\alpha:[0,1]\\to{\\mathcal S}$ whose image meets all the connected components of the set of regular points of ${\\mathcal S}$. Some remarkable consequences are the following: (1) pure dimensional irreducible "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05706","kind":"arxiv","version":8},"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"}