Conference on Computability in Europe

CiE 2013: The Nature of Computation. Logic, Algorithms, Applications pp 294-305

Closed Choice for Finite and for Convex Sets

  • Stéphane Le Roux
  • Arno Pauly
Conference paper

DOI: 10.1007/978-3-642-39053-1_34

Volume 7921 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Le Roux S., Pauly A. (2013) Closed Choice for Finite and for Convex Sets. In: Bonizzoni P., Brattka V., Löwe B. (eds) The Nature of Computation. Logic, Algorithms, Applications. CiE 2013. Lecture Notes in Computer Science, vol 7921. Springer, Berlin, Heidelberg

Abstract

We investigate choice principles in the Weihrauch lattice for finite sets on the one hand, and convex sets on the other hand. Increasing cardinality and increasing dimension both correspond to increasing Weihrauch degrees. Moreover, we demonstrate that the dimension of convex sets can be characterized by the cardinality of finite sets encodable into them. Precisely, choice from an n + 1 point set is reducible to choice from a convex set of dimension n, but not reducible to choice from a convex set of dimension n − 1.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Stéphane Le Roux
    • 1
  • Arno Pauly
    • 2
  1. 1.Department of MathematicsTechnische Universität DarmstadtGermany
  2. 2.Clare CollegeUniversity of CambridgeUnited Kingdom