A counterexample to Borsuk’s conjecture

Publisher Website

1 July 1993

journal article
Published by American Mathematical Society (AMS) in Bulletin of the American Mathematical Society

Vol. 29 (1) , 60-62
https://doi.org/10.1090/s0273-0979-1993-00398-7

Abstract

Let

f(d)

be the smallest number so that every set in

{R^d}

of diameter 1 can be partitioned into

f(d)

sets of diameter smaller than 1. Borsuk’s conjecture was that

f(d) = d + 1

. We prove that

f(d) \geq (1.2)\sqrt d

for larged.

Keywords

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