{"paper":{"title":"Oscillation Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Gerald Beer, Jiling Cao","submitted_at":"2016-08-10T04:39:34Z","abstract_excerpt":"In previous work by Beer and Levi [8, 9], the authors studied the oscillation $\\Omega (f,A)$ of a function $f$ between metric spaces $\\langle X,d \\rangle$ and $\\langle Y,\\rho \\rangle$ at a nonempty subset $A$ of $X$, defined so that when $A =\\{x\\}$, we get $\\Omega (f,\\{x\\}) = \\omega (f,x)$, where $\\omega (f,x)$ denotes the classical notion of oscillation of $f$ at the point $x \\in X$. The main purpose of this article is to formulate a general joint continuity result for $(f,A) \\mapsto \\Omega (f,A)$ valid for continuous functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03043","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"}