Equivalent forms of the Brouwer fixed point theorem
KeywordsBorsuk non-retraction theorem, Himmelberg fixed point theorem, Nash equilibrium, Maynard Smith Theorem, KKM lemma
AbstractIn 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.
How to Cite
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].
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