Abstract
In this short note a simple and constructive proof is given for Borsuk's theorem on antipodal points. This is done through a special application of the complementary pivoting algorithm.
References
I. Bárány, “A short proof of Kneser's conjecture”,Journal of Combinatorial Theory 25 (1978) 325–326.
K. Borsuk, “Drei Sätze über dien-dimensionalische euklidische Sphäre”,Fundamenta Mathematicae 20 (1933) 177–190.
F.E. Browder, “On continuity of fixed points under deformations of continuous mappings”,Summa Brasiliensis Mathematicae 4 (1960) 183–191.
B.C. Eaves, “A short course in solving equations with PL homotopies”SIAM-AMS Proceedings 9 (1976) 73–143.
L. Lovász, “Kneser's conjecture, chromatic number and homotopy”,Journal of Combinatorial Theory 25 (1978) 319–324.
M.J. Todd,The computation of fixed points and applications (Springer, Berlin, 1976).
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Bárány, I. Borsuk's theorem through complementary pivoting. Mathematical Programming 18, 84–88 (1980). https://doi.org/10.1007/BF01588299
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DOI: https://doi.org/10.1007/BF01588299