{"paper":{"title":"Roberts' type embeddings and conversion of the transversal Tverberg's theorem","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GN","authors_text":"Semeon Bogatyi, Vesko Valov","submitted_at":"2005-03-07T21:36:12Z","abstract_excerpt":"Here are two of our main results: Theorem 1. Let X be a normal space with dim X=n and m\\geq n+1. Then the space C*(X,R^m) of all bounded maps from X into R^m equipped with the uniform convergence topology contains a dense G_{\\delta}-subset consisting of maps g such that \\bar{g(X)}\\cap\\Pi^d is at most (n+d-m)-dimensional for every d-dimensional plane \\Pi^d in R^m, where m-n\\leq d\\leq m.\n  Theorem 2. Let X be a metrizable compactum with dim X\\leq n and m\\geq n+1. Then, C(X,R^m) contains a dense G_{\\delta}-subset of maps g such that for any integers t,d,T with 0\\leq t\\leq d\\leq m-n-1 and d\\leq T\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503131","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"}