## Equivalence between Sperenr’s lemma and Brouwer’s fixed point theorem [closed]

Hey,

I'm writhing my bachelor thesis in mathematics and I'm stuck at finding a proof for Sperner's lemma using Brouwer's fixed point theorem. I need it to prove the equivalence of the two theorems.

I would appreciate any help in finding a proof.

1. Take the map which projects the vertex of color $n$ to the opposite side. 2. Extend this map linearly to all simplices. 3. Think. (I vote to close.) – Anton Petrunin Jul 29 at 12:42