{"paper":{"title":"Special embeddings of finite-dimensional compacta in Euclidean spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"S. Bogatyi, V. Valov","submitted_at":"2010-10-23T01:47:06Z","abstract_excerpt":"If $g$ is a map from a space $X$ into $\\mathbb R^m$ and $z\\not\\in g(X)$, let $P_{2,1,m}(g,z)$ be the set of all lines $\\Pi^1\\subset\\mathbb R^m$ containing $z$ such that $|g^{-1}(\\Pi^1)|\\geq 2$. We prove that for any $n$-dimensional metric compactum $X$ the functions $g\\colon X\\to\\mathbb R^m$, where $m\\geq 2n+1$, with $\\dim P_{2,1,m}(g,z)\\leq 0$ for all $z\\not\\in g(X)$ form a dense $G_\\delta$-subset of the function space $C(X,\\mathbb R^m)$. A parametric version of the above theorem is also provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4838","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"}