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Infinite Powers and Cohen Reals

Published online by Cambridge University Press:  20 November 2018

Andrea Medini ,
Jan van Mill  and
Lyubomyr Zdomskyy
Andrea Medini
Affiliation:
Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Strasse 25, A-1090 Wien, Austria, e-mail : andrea.medini@univie.ac.at , lyubomyr.zdomskyy@univie.ac.at
Jan van Mill
Affiliation:
Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, P. O. Box 94248, 1090 GE Amsterdam, Netherlands, e-mail : j.vanmill@uva.nl
Lyubomyr Zdomskyy
Affiliation:
Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Strasse 25, A-1090 Wien, Austria, e-mail : andrea.medini@univie.ac.at , lyubomyr.zdomskyy@univie.ac.at
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Abstract

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

Keywords

03E3554B1054G20infinite powerzero-dimensionalfirst-countablehomogeneousCohen realrigidh-homogeneous
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 4 , 01 December 2018 , pp. 812 - 821
Copyright
Copyright © Canadian Mathematical Society 2018

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