On the Two-Dimensional Version of the Sperner Lemma and Brouwer’s Theorem

Abstract

In this work the Brouwer fixed point theorem for a triangle was proved by two methods based on the Sperner Lemma. One of the two proofs of Sperner’s Lemma given in the paper was carried out using the so-called index.

Keywords

• sperner’s lemma
• brouwer’s theorem
• retraction
• fixed-point property
• 47h10
• 54h25
• 05c90