Beer, GCao, J2016-09-182016-09-182016-08-102016-08-10arXiv:1608.03043 [math.GN]https://hdl.handle.net/10292/10029In previous work by Beer and Levi [8, 9], the authors studied the oscillation Ω(f, A) of a function f between metric spaces hX, di and hY, ρi at a nonempty subset A of X, defined so that when A = {x}, we get Ω(f, {x}) = ω(f, x), where ω(f, x) denotes the classical notion of oscillation of f at the point x ∈ X. The main purpose of this article is to formulate a general joint continuity result for (f, A) 7→ Ω(f, A) valid for continuous functions.Granting rights for arXiv to distribute an article does not preclude later copyright assignment. Authors are thus free to publish submissions that already appear on arXiv. Authors may wish to inform the journal publisher that a prior non-exclusive license exists before transferring copyright or granting a publication license. Please check the policies of any potential publication venue before uploading to arXiv. (For the policy information of many publishers, see the SHERPA/RoMEO site.)OscillationStrong uniform continuityUC-subset Hausdorff distanceLocally finite topologyFinite topologyStrong uniform convergenceVery strong uniform convergenceBornologyCommissioned ReportOpenAccess