On Aumann's Theorem that the sphere does not admit a mean
General Topology
2013-10-08 v1
Abstract
We prove that the circle S_1 does not have a 2-mean, i.e., S_1 times S_1 cannot have a retraction r onto its diagonal with r(x,y) = r(y,x), whenever x,y in S_1. Our proof is combinatorial and topological rather than analytical.
Cite
@article{arxiv.math/0501305,
title = {On Aumann's Theorem that the sphere does not admit a mean},
author = {F. Javier Trigos-Arrieta and Marian Turzanski},
journal= {arXiv preprint arXiv:math/0501305},
year = {2013}
}
Comments
6 pages