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Brouwer's theorem for a square on the basis of Hex theorem

Barcz Eugeniusz

Silesian Journal of Pure and Applied Mathematics

2022

Vol. 12, iss. 1

33--44

This work is a continuation of author's work [1] on fixed points. In this work, Brouwer's theorem is proved on the basis of the Hex theorem. In the proof, the author uses, among other things, the lemma about no draw. Two proofs of this lemma are derived. The second proof is a modification of D. Gale's proof [2] and is based on the concept of a walk on the Hex board.