Published online by Cambridge University Press: 20 November 2018
We give a consistent example of a zero-dimensional separable metrizable space $Z$ such that every homeomorphism of
${{Z}^{\omega }}$ 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
${{\omega }_{1}}$ Cohen reals, viewed as a subspace of
${{2}^{\omega }}$.