Geodesic
Infinite Powers and Cohen Reals
Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 812-821

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DOI

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 ${{2}^{\omega }}$ .
DOI : 10.4153/CMB-2017-055-x
Mots-clés : 03E35, 54B10, 54G20, infinite power, zero-dimensional, first-countable, homogeneous, Cohen real, rigid, h-homogeneous 
Medini, Andrea; Mill, Jan van; Zdomskyy, Lyubomyr. Infinite Powers and Cohen Reals. Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 812-821. doi: 10.4153/CMB-2017-055-x
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     title = {Infinite {Powers} and {Cohen} {Reals}},
     journal = {Canadian mathematical bulletin},
     pages = {812--821},
     year = {2018},
     volume = {61},
     number = {4},
     doi = {10.4153/CMB-2017-055-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-055-x/}
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