{"paper":{"title":"Sobolev Embedding of a Sphere Containing An Arbitrary Cantor Set in the image","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Piotr Haj{\\l}asz, Xiaodan Zhou","submitted_at":"2015-07-19T18:47:21Z","abstract_excerpt":"We construct a large class of pathological $n$-dimensional topological spheres in ${\\mathbb R}^{n+1}$ by showing that for any Cantor set $C\\subset {\\mathbb R}^{n+1}$ there is a topological embedding $f:{\\mathbb S}^n\\to{\\mathbb R}^{n+1}$ of the Sobolev class $W^{1,n}$ whose image contains the Cantor set $C$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05319","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"}