{"paper":{"title":"Hurewicz Theorem for Assouad-Nagata dimension","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.MG","authors_text":"A.Mitra, J.Dydak, M.Levin, N.Brodskiy","submitted_at":"2006-05-16T07:03:36Z","abstract_excerpt":"Given a function $f\\colon X\\to Y$ of metric spaces, its {\\it asymptotic dimension} $\\asdim(f)$ is the supremum of $\\asdim(A)$ such that $A\\subset X$ and $\\asdim(f(A))=0$. Our main result is \\begin{Thm} \\label{ThmAInAbstract} $\\asdim(X)\\leq \\asdim(f)+\\asdim(Y)$ for any large scale uniform function $f\\colon X\\to Y$. \\end{Thm}\n  \\ref{ThmAInAbstract} generalizes a result of Bell and Dranishnikov in which $f$ is Lipschitz and $X$ is geodesic. We provide analogs of \\ref{ThmAInAbstract} for Assouad-Nagata dimension $\\dim_{AN}$ and asymptotic Assouad-Nagata dimension $\\ANasdim$. In case of linearly co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605416","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"}