{"paper":{"title":"A fixed-point-free map of a tree-like continuum induced by bounded valence maps on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"L. C. Hoehn, Rodrigo Hern\\'andez-Guti\\'errez","submitted_at":"2016-08-29T14:58:25Z","abstract_excerpt":"Towards attaining a better working understanding of fixed points of maps of tree-like continua, Oversteegen and Rogers constructed a tree-like continuum with a fixed-point-free self-map, described explicitly in terms of inverse limits. Specifically, they developed a sequence of trees $T_n$, $n \\in \\mathbb{N}$ and maps $f_n$ and $g_n$ from $T_{n+1}$ to $T_n$ for each $n$, such that the $g_n$ maps induce a fixed-point-free self-map of the inverse limit space $\\varprojlim (T_n,f_n)$.\n  The complexity of the trees and the valences of the maps in their example all grow exponentially with $n$, makin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08094","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"}