Topological Methods in Nonlinear Analysis

Equivalent forms of the Brouwer fixed point theorem I

Adam Idzik, Władysław Kulpa, and Piotr Maćkowiak

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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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 44, Number 1 (2014), 263-276.

Dates
First available in Project Euclid: 11 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1460381481

Mathematical Reviews number (MathSciNet)
MR3289019

Zentralblatt MATH identifier
06700618

Citation

Idzik, Adam; Kulpa, Władysław; Maćkowiak, Piotr. Equivalent forms of the Brouwer fixed point theorem I. Topol. Methods Nonlinear Anal. 44 (2014), no. 1, 263--276. https://projecteuclid.org/euclid.tmna/1460381481


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