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Infinite powers and Cohen reals

  • Andrea Medini,
    Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Strasse 25, A-1090 Wien, Austria
  • Jan van Mill,
    Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 105-107, P. O. Box 94248, 1090 GE Amsterdam, Netherlands
  • Lyubomyr S. Zdomskyy,
    Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Strasse 25, A-1090 Wien, Austria
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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 $2^\omega$.
Keywords: infinite power, zero-dimensional, first-countable, homogeneous, Cohen real, h-homogeneous, rigid infinite power, zero-dimensional, first-countable, homogeneous, Cohen real, h-homogeneous, rigid
MSC Classifications: 03E35, 54B10, 54G20 show english descriptions Consistency and independence results
Product spaces
Counterexamples
03E35 - Consistency and independence results
54B10 - Product spaces
54G20 - Counterexamples
 

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