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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0605416","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.MG","submitted_at":"2006-05-16T07:03:36Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"390a097e594238dc7532e716b3994a4efcbee2b899a7d281c504a0db88e87af7","abstract_canon_sha256":"889be192fd994f3a317e950906e7afbc17673bd1a9efbd3c93d0406e07f26711"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:45.593620Z","signature_b64":"0Joy67YbOKsKetptPP35yFza+LJyTzLCdkH0ipcSFrwXluzG6ZUw1TLcsrlkQ/mAefW1N8NQSSCjQC50AfHnAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2adb52356a8c9e730c8dc06c90ec2628bd44d100fa1642095482b63ccc1aa545","last_reissued_at":"2026-05-18T02:57:45.593142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:45.593142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\ANasdim$. 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