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
References
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J. Milnor, Analytic proofs of the “Hairy Ball Theorem” and the Brouwer Fixed Point Theorem, Amer. Math. Monthly 85 (1978), no. 7, 521–524.
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D. Violette, Applications du lemme de Sperner pour les triangles, Bulletin AMQ 46 (2006), no. 4, 12–19.
Uniwersytet Warmińsko-Mazurski w Olsztynie, Wydział Matematyki i Informatyki, Katedra Analizy Zespolonej Poland
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