Equivalent forms of the Brouwer fixed point theorem

Adam Idzik, Władysław Kulpa, Piotr Maćkowiak

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.

Keywords


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

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