{"paper":{"title":"$1/k$-homogeneous long solenoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Gary Gruenhage, George Kozlowski, Jan P. Boronski","submitted_at":"2014-12-29T23:17:44Z","abstract_excerpt":"We study nonmetric analogues of Vietoris solenoids. Let $\\Lambda$ be an ordered continuum, and let $\\vec{p}=\\langle p_1,p_2,\\dots\\rangle$ be a sequence of positive integers. We define a natural inverse limit space $S(\\Lambda,\\vec{p})$, where the first factor space is the nonmetric \"circle\" obtained by identifying the endpoints of $\\Lambda$, and the $n$th factor space, $n>1$, consists of $p_1p_2\\cdot\\dots \\cdot p_{n-1}$ copies of $\\Lambda$ laid end to end in a circle. We prove that for every cardinal $\\kappa\\geq 1$, there is an ordered continuum $\\Lambda$ such that $S(\\Lambda,\\vec{p})$ is $\\fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8508","kind":"arxiv","version":2},"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"}