{"paper":{"title":"Decompositions of $\\mathbb{R}^n, n \\geq 4,$ into convex sets generate codimension 1 manifold factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GT","authors_text":"Denise M. Halverson, Du\\v{s}an Repov\\v{s}","submitted_at":"2013-04-25T16:35:30Z","abstract_excerpt":"We show that if $G$ is an upper semicontinuous decomposition of $\\mathbb{R}^n$, $n \\geq 4$, into convex sets, then the quotient space $\\mathbb{R}^n/G$ is a codimension one manifold factor. In particular, we show that $\\mathbb{R}^n/G$ has the disjoint arc-disk property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6956","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"}