{"paper":{"title":"Periodic and fixed points of multivalued maps on Euclidean spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"A. Chigogidze, R. Z. Buzyakova","submitted_at":"2012-02-07T22:06:24Z","abstract_excerpt":"We show, in particular, that a multivalued map $f$ from a closed subspace $X$ of $\\mathbb R^n$ to ${\\rm exp}_k(\\mathbb R^n)$ has a point of period exactly $M$ if and only if its continuous extension $\\tilde f: \\beta X\\to {\\rm exp}_k(\\beta \\mathbb R^n)$ has such a point. The result also holds if one repace $\\mathbb R^n$ by a locally compact Lindel\\\"of space of finite dimension. We also show that if $f$ is a colorable map froma normal space $X$ to the space ${\\mathcal K}(X)$ of all compact subsets of $X$ then its extension $\\tilde f:\\beta X\\to {\\mathcal K}(\\beta X)$ is fixed-point free."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1544","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"}