{"paper":{"title":"Uniform disconnectedness and Quasi-Assouad Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Fan L\\\"u, Li-Feng Xi","submitted_at":"2014-09-07T00:04:18Z","abstract_excerpt":"The uniform disconnectedness is an important invariant property under bi-Lipschitz mapping, and the Assouad dimension $\\dim _{A}X<1$ implies the uniform disconnectedness of $X$. According to quasi-Lipschitz mapping, we introduce the quasi-Assouad dimension $\\dim _{qA}$ such that $\\dim _{qA}X<1$ implies its quasi uniform disconnectedness. We obtain $\\overline{\\dim } _{B}X\\leq \\dim _{qA}X\\leq \\dim _{A}X$ and compute the quasi-Assouad dimension of Moran set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2070","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"}