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Infinite Powers and Cohen Reals
Published online by Cambridge University Press: 20 November 2018
Abstract
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 ${{2}^{\omega }}$.
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- Copyright © Canadian Mathematical Society 2018
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