Infinite Powers and Cohen Reals. Issue 4 (1st December 2018) - Medini, Andrea; van Mill, Jan; Zdomskyy, Lyubomyr
Abstract: We give a consistent example of a zero-dimensional separable metrizable space $Z$ such that every homeomorphism of ${Z^{ω }}$ 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 ${{ω }_{1}}$ Cohen reals, viewed as a subspace of ${{2}^{ω }}$ .