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.
Create a lesson
Related papers
Hereditarily Lindelöf and hereditarily separable subspaces of function spaces
Evgenii Reznichenko
Separately continuous maps into regular spaces and continuity of operations in separable semitopological groups
Evgenii Reznichenko
Four problems about the irreducible determined T0-topologies
Chongyun Zhao, Xiaoquan Xu
Nonpathological submeasures and Fσ ideals
Paolo Leonetti
On Separately Continuous Functions of the First Baire Class on Squares and Mixed Products
Alexander V. Osipov
Uniform retractions onto a probability measure algebra and an application to topological groups
Dekui Peng, Li-Hong Xie, Jiang Yang