Infinite Powers and Cohen Reals
Printed: Dec 2018
Jan van Mill,
Lyubomyr S. Zdomskyy,
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 $2^\omega$.
infinite power, zero-dimensional, first-countable, homogeneous, Cohen real, h-homogeneous, rigid
03E35 - Consistency and independence results
54B10 - Product spaces
54G20 - Counterexamples