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Monovex sets

Volume 242 / 2018

Lev Buhovsky, Eilon Solan, Omri N. Solan Studia Mathematica 242 (2018), 165-178 MSC: Primary 52A30; Secondary 47H10. DOI: 10.4064/sm8765-7-2017 Published online: 5 February 2018

Abstract

A set $A$ in a finite-dimensional Euclidean space is monovex if for any $x,y \in A$ there is a continuous path within $A$ that connects $x$ and $y$ and is monotone (nonincreasing or nondecreasing) in each coordinate. We prove that every open monovex set and every closed monovex set are contractible, and we provide an example of a nonopen and nonclosed monovex set that is not contractible. Our proofs reveal additional properties of monovex sets.

Authors

  • Lev BuhovskySchool of Mathematical Sciences
    Tel Aviv University
    Tel Aviv 6997800, Israel
    e-mail
  • Eilon SolanSchool of Mathematical Sciences
    Tel Aviv University
    Tel Aviv 6997800, Israel
    e-mail
  • Omri N. SolanSchool of Mathematical Sciences
    Tel Aviv University
    Tel Aviv 6997800, Israel
    e-mail

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