Logicism, Intuitionism, and Formalism pp 277-299

Part of the Synthese Library book series (SYLI, volume 341) | Cite as

Brouwer’s Approximate Fixed-Point Theorem is Equivalent to Brouwer’s Fan Theorem

  • Wim Veldman

Abstract

In a weak system for intuitionistic analysis, one may prove, using the Fan Theorem as an additional axiom, that, for every continuous function ø from the unit square U to itself, for every positive rational e, there exists x in U such that |ø(x) − x| < e. Conversely, if this statement is taken as an additional axiom, the Fan Theorem follows.

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Wim Veldman
    • 1
  1. 1.Institute for Mathematics Astrophysics and Particle Physics Faculty of ScienceRadboud University Nijmegenthe Netherlands

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