Equivalent forms of the Brouwer fixed point theorem

Authors

  • Adam Idzik
  • Władysław Kulpa
  • Piotr Maćkowiak

Keywords

Borsuk non-retraction theorem, Himmelberg fixed point theorem, Nash equilibrium, Maynard Smith Theorem, KKM lemma

Abstract

In this paper we survey a set of Brouwer fixed point theorem equivalents. These equivalents are divided into four loops related to (1) the Borsuk retraction theorem, (2) the Himmelberg fixed point theorem, (3) the Gale lemma and (4) the Nash equilibrium theorem.

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Published

2016-04-12

How to Cite

1.
IDZIK, Adam, KULPA, Władysław & MAĆKOWIAK, Piotr. Equivalent forms of the Brouwer fixed point theorem. Topological Methods in Nonlinear Analysis [online]. 12 April 2016, T. 44, nr 1, s. 263–276. [accessed 31.1.2023].

Issue

Vol 44, No 1 (September 2014)

Section

Articles

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