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I'm looking for a proof that Brouwer's fixed point theorem implies Sperner's lemma. The proof should be understandable by an undergraduate.

Thanks in advance!

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For reverse direction, see Proofs in the Book pg ~148. –  sdcvvc Aug 7 '12 at 17:54

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A simple proof can be found in a paper by Park and Jeong:
A PROOF OF THE SPERNER LEMMA FROM THE BROUWER FIXED POINT THEOREM Nonlinear Analysis Forum 8(1), pp. 65–67, 2003 (available from http://www.na-forum.org/)

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