Adam Idzik, W. 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.
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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.
Key concepts: Mathematics, Kakutani fixed-point theorem, Brouwer fixed-point theorem, Fixed-point theorem, Lefschetz fixed-point theorem, Fixed-point property, Picard–Lindelöf theorem, Schauder fixed point theorem