Inverse limit means are not preserved under homeomorphisms
A mean is just a symmetric and idempotent continuous binary law on a topological space. It is possible to construct means in various ways, for example in the case of an inverse limit space, from means built on each coordinate space. At least if some functional compatibility condition is valid for each coordinate [\textit{J. A. Baker} and the author, Aequationes Math. 26, 89-103 (1983; Zbl 0536.39005)]. A natural question is to see if all means on an inverse limit space are built in the way described. The present and short paper answers ``no'', in a rather general case using a simple example. It can be seen as the impossibility of a solution for an infinite system of functional equations.
symmetric and idempotent continuous binary law
scientific article; zbMATH DE number 4150998