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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Journal of modern dynamics, American Institute of Mathematical Sciences, 2016, 〈10.3934/jmd.2016.10.331〉
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-01412052
Contributeur : Albert Fathi <>
Soumis le : mercredi 7 décembre 2016 - 19:01:30
Dernière modification le : jeudi 11 janvier 2018 - 06:12:31

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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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