  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 $2^\omega$.
