Abstract
We give a proof of Tucker’s Combinatorial Lemma that proves the fundamental nonexistence theorem: There exists no continuous map fromB n toS n − 1 that maps antipodal points of∂B n to antipodal points ofS n − 1.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Baranyi,A short proof of Kneser’s conjecture, J. Comb. Theory, Ser. A25 (1978), 325–326.
L. Dubins and G. Schwarz,Equidis continuity of Borsuk — Ulam functions, Pacific J. Math.95 (1981), 51–59.
Ky Fan,A generalization of Tucker’s combinatorial lemma with topological applications, Ann. of Math.56 (1952), 431–437.
S. Lefschetz,Introduction to Topology, Princeton University Press, 1949.
L. Lovász,Kneser’s conjecture, chromatic number and homotopy, J. Comb. Theory, Ser. A25 (1978), 319–324.
A. W. Tucker,Some topological properties of disk and sphere, Proceedings of First Canadian Mathematical Congress, Toronto University Press, 1946, pp. 285–309.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Weiss, B. A combinatorial proof of the Borsuk-Ulam antipodal point theorem. Israel J. Math. 66, 364–368 (1989). https://doi.org/10.1007/BF02765904
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02765904