On Aumann's Theorem that the sphere does not admit a mean
F. Javier Trigos-Arrieta, Marian Turzanski
Abstract
We prove that the circle S1 does not have a 2-mean, i.e., S1 times S1 cannot have a retraction r onto its diagonal with r(x,y) = r(y,x), whenever x,y in S1. Our proof is combinatorial and topological rather than analytical.
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