CONTROLLING LIPSCHITZ FUNCTIONS

Andrey Kupavskii, János Pach, Gábor Tardos

Research output: Contribution to journalArticle

Abstract

Given any positive integers m and d, we say a sequence of points (x i ) i∈I in R m is Lipschitz-d-controlling if one can select suitable values yi (i ∈ I) such that for every Lipschitz function f :R m →R d there exists i with /f (x i ) - y i /<1. We conjecture that for every m = d, a sequence (x i ) i∈I ⊂ R m is d-controlling if and only if [Equation presented here] We prove that this condition is necessary and a slightly stronger one is already sufficient for the sequence to be d-controlling. We also prove the conjecture for m = 1.

Original languageEnglish
Pages (from-to)898-910
Number of pages13
JournalMathematika
Volume64
Issue number3
DOIs
Publication statusPublished - Jan 1 2018

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ASJC Scopus subject areas

  • Mathematics(all)

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