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An Urysohn-type theorem under a dynamical constraint

Abstract : We address the following question raised by M. Entov and L. Polterovich: given a continuous map f:X→X of a metric space X, closed subsets A,B⊂X, and an integer n≥1, when is it possible to find a continuous function θ:X→ℝ such that θf−θ≤1,θ∣∣A≤0,andθ∣∣B>n? To keep things as simple as possible, we solve the problem when A is compact. The non-compact case will be treated in a later work.
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Contributor : Albert Fathi <>
Submitted on : Wednesday, December 7, 2016 - 7:01:30 PM
Last modification on : Tuesday, December 8, 2020 - 10:03:59 AM

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Albert Fathi. An Urysohn-type theorem under a dynamical constraint. Journal of modern dynamics, American Institute of Mathematical Sciences, 2016, ⟨10.3934/jmd.2016.10.331⟩. ⟨ensl-01412052⟩



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