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  • School of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, Pāngarau
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Oscillation Revisited

Beer, G; Cao, J
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1608.03043v1.pdf (195.2Kb)
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http://hdl.handle.net/10292/10029
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Abstract
In 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.
Keywords
Oscillation; Strong uniform continuity; UC-subset Hausdorff distance; Locally finite topology; Finite topology; Strong uniform convergence; Very strong uniform convergence; Bornology
Date
August 10, 2016
Source
arXiv:1608.03043 [math.GN]
Item Type
Commissioned Report
Publisher
arXiv
Publisher's Version
http://arxiv.org/abs/1608.03043
Rights Statement
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.)

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