Sperner's Lemma and Brouwer's Fixed-Point Theorem


Joel H. Shapiro

 

Lecture Notes, April 2015
 
Abstract: Notes for a lecture I gave at the Portland State University Analysis Seminar during the Spring term 2015. They present a proof of the Brouwer Fixed-Point Theorem using a remarkable combinatorial lemma due to Emanuel Sperner. The method works in RN for all N, but for simplicity the discussion is restricted to N=2.

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