Topology Atlas Document # paao-46
We prove that the circle S1 does not have a 2-mean, i.e., S1×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.
Date received: November 20, 2003.
Copyright © 2003 by the authors. Distributed by Topology Atlas with permission of the authors.