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 Stanislaw Ulam) that is now known as the Borsuk-Ulam theorem:
Every continuous map f: Sd —> ℝd maps two antipodal points of the sphere Sd to the same point in ℝd.
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References
K. Borsuk: Drei Sätze über die n-dimensionale euklidische Sphäre, Fundamenta Math. 20 (1933), 177 - 190.
J. Kahn & G. Kalai: A counterexample to Borsuk’s conjecture, Bulletin 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. Math. Soc. 1994, 209 - 210.
A. M. Raigorodskii: O razmernosti v probleme Borsuka (A counterexample for Borsuk’s problem; in Russian), Uspekhi Mat. Nauk (6)52 (1997), 181 - 182.
O. Schramm: Illuminating sets of constant width, Mathematika 35 (1988), 180 - 199.
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© 1998 Springer-Verlag Berlin Heidelberg
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Aigner, M., Ziegler, G.M. (1998). Borsuk’s conjecture. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-22343-7_15
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DOI: https://doi.org/10.1007/978-3-662-22343-7_15
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