Infinite Powers and Cohen Reals

Abstract

AbstractWe give a consistent example of a zero-dimensional separable metrizable space Z such that every homeomorphism of Zω acts like a permutation of the coordinates almost everywhere. Furthermore, this permutation varies continuously. This shows that a result of Dow and Pearl is sharp, and gives some insight into an open problem of Terada. Our example Z is simply the set of ω1 Cohen reals, viewed as a subspace of 2ω.