Geodesic
On a discrete version of the antipodal theorem
Fundamenta Mathematicae, Tome 151 (1996) no. 2, pp. 189-194.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The classical theorem of Borsuk and Ulam [2] says that for any continuous mapping $f: S^k → ℝ^k$ there exists a point $x ∈ S^k$ such that f(-x) = f(x). In this note a discrete version of the antipodal theorem is proved in which $S^k$ is replaced by the set of vertices of a high-dimensional cube equipped with Hamming's metric. In place of equality we obtain some optimal estimates of $inf_x ||f(x)-f(-x)||$ which were previously known (as far as the author knows) only for f linear (cf. [1]).
DOI : 10.4064/fm-151-2-189-194

Krzysztof Oleszkiewicz 1

1 
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Krzysztof Oleszkiewicz. On a discrete version of the antipodal theorem. Fundamenta Mathematicae, Tome 151 (1996) no. 2, pp. 189-194. doi : 10.4064/fm-151-2-189-194. http://geodesic.mathdoc.fr/articles/10.4064/fm-151-2-189-194/

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