Inverse limit means are not preserved under homeomorphisms
type: Item
instance of: scholarly article
title: Inverse limit means are not preserved under homeomorphisms
zbMATH Open document ID: 0702.39006
DOI: 10.1216/RMJ-1989-19-2-549
author: B. E. Wilder
published in: Rocky Mountain Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 39B62
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 54A20
zbMATH DE Number: 4150998
zbMATH Keywords: mean
zbMATH Keywords: symmetric and idempotent continuous binary law
zbMATH Keywords: topological space
zbMATH Keywords: inverse limit space
zbMATH Keywords: coordinate space
zbMATH Keywords: infinite system of functional equations
reviewed by: Jean Dhombres
MaRDI profile type: Publication
full work available at URL: rmj-1989-19-2-549
OpenAlex ID: W1990256578
description: scientific article; zbMATH DE number 4150998