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This result was improved by J.H.G. Fu (1985). We show that Ferry's result is an easy consequence of the only fact that the distance function $d(x)= \\dist(x,F)$ is locally DC and has no stationary point in $\\R^n\\setminus F$. Using this observation, we show that Ferry's (and even Fu's) result extends to sufficiently smooth normed linear spaces $X$ with"},"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":"0911.4020","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-11-20T11:42:32Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"a83d7a8f17341e1169bcda361a75627c4ee942842411fe431a0b6e8db0be25d5","abstract_canon_sha256":"cfd97db5ccb503f64e498e87e326c6378162024afec114b3ddbcf4c5b94b04ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:29.196243Z","signature_b64":"xyVt/IhotKp9WwFhPqeH5Q4MKdHX4SHrnR/IEe3kX69073O35/XAIRyvUKDCmEDTyngCHZ9QLzi8Zz/81KP4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbd10a4cf0665c71feea5515b0d6fa9d20eb71dc507594da6823a9701314b87b","last_reissued_at":"2026-05-18T03:37:29.195480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:29.195480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical values and level sets of distance functions in Riemannian, Alexandrov and Minkowski spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Jan Rataj, Ludek Zajicek","submitted_at":"2009-11-20T11:42:32Z","abstract_excerpt":"Let $F \\subset \\R^n$ be a closed set and $n=2$ or $n=3$. 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