{"paper":{"title":"Remarks on WDC sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Du\\v{s}an Pokorn\\'y, Lud\\v{e}k Zaj\\'i\\v{c}ek","submitted_at":"2019-05-29T20:31:45Z","abstract_excerpt":"We study WDC sets, which form a substantial generalization of sets with positive reach and still admit the definition of curvature measures. Main results concern WDC sets $A\\subset \\mathbb{R}^2$. We prove that, for such $A$, the distance function $d_A= {\\rm dist}(\\cdot,A)$ is a `DC aura' for $A$, which implies that each locally WDC set in $\\mathbb{R}^2$ is a WDC set. An another consequence is that compact WDC subsets of $\\mathbb{R}^2$ form a Borel subset of the space of all compact sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12709","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"}