{"paper":{"title":"On multivaled fixed-point free maps on R^n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Raushan Buzyakova","submitted_at":"2012-06-13T14:30:05Z","abstract_excerpt":"To formulate our results let $f$ be a continuous map from $\\mathbb R^n$ to $2^{\\mathbb R^n}$ and $k$ a natural number such that $|f(x)|\\leq k$ for all $x$. We prove that $f$ is fixed-point free if and only if its continuous extension $\\tilde f:\\beta \\mathbb R^n\\to 2^{\\beta \\mathbb R^n}$ is fixed-point free. If one wishes to stay within metric terms, the result can be formulated as follows: $f$ is fixed-point free if and only if there exists a continuous fixed-point free extension $\\bar f: b\\mathbb R^n\\to 2^{b\\mathbb R^n}$ for some metric compactificaton $b\\mathbb R^n$ of $\\mathbb R^n$. Using t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2820","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"}