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

Author:

Barcz Eugeniusz1

Affiliation:

1. University of Warmia and Mazury , Faculty of Mathematics and Computer Science, Chair of Complex Analysis , Słoneczna 54 Street Olsztyn Poland

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference4 articles.

1. [1] E. Barcz, Local versions of Banach principle, their generalizations and applications, in: A. Lecko (ed.), Courrent Research in Mathematical and Computer Sciences, Wydawnictwo UWM, Olsztyn, 2017, pp. 41–53.

2. [2] J. Milnor, Analytic proofs of the “Hairy Ball Theorem” and the Brouwer Fixed Point Theorem, Amer. Math. Monthly 85 (1978), no. 7, 521–524.

3. [3] Yu.A. Shashkin, Fixed Points, Mathematical World, 2, AMS, Providence & MAA, Washington, 1991.10.1090/mawrld/002

4. [4] D. Violette, Applications du lemme de Sperner pour les triangles, Bulletin AMQ 46 (2006), no. 4, 12–19.

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