Abstract
Karol Borsuk’s paper “Three theorems on the n-dimensional euclidean sphere” from 1933 is famous because it contained an important result (conjectured by Stanisław Ulam) that is now known as the Borsuk-Ulam theorem:
Every continuous map f: S d → ℝd maps two antipodal points of the sphere S d to the same point in ℝd.
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References
K. Borsuk: Drei Sätze über die n-dimensionale euklidische Sphäre, Fund; menta Math. 20 (1933), 177–190.
A. Hinrichs & C. Richter: New sets with large Borsuk numbers, Preprir February 2002, 10 pages.
J. Kahn & G. Kalai: A counterexample to Borsuk’s conjecture, Bullet: Amer. Math. Soc. 29 (1993), 60–62.
A. Nilli: On Borsuk’s problem, in: “Jerusalem Combinatorics’ 93 (H. Barcelo and G. Kalai, eds.), Contemporary Mathematics 178, Amer. Mat Soc. 1994, 209-210.
A. M. Raigorodskii: On the dimension in Borsuk’s problem, Russian Mat-Surveys (6) 52 (1997), 1324–1325.
O. Schramm: Illuminating sets of constant width, Mathematika 35 (1988) 180–199.
B. Weissbach: Sets with large Borsuk number, Beiträge zur Algebra ur Geometrie/Contributions to Algebra and Geometry 41 (2000), 417–423.
G. M. Ziegler: Coloring Hamming graphs, optimal binary codes, and tl 0/1-Borsuk problem in low dimensions, Lecture Notes in Computer Science 2122, Springer-Verlag 2001, 164-175.
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Aigner, M., Ziegler, G.M. (2001). Borsuk’s conjecture. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04315-8_14
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DOI: https://doi.org/10.1007/978-3-662-04315-8_14
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