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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 
${{2}^{\omega }}$.
