Infinite Powers and Cohen Reals
نویسنده
چکیده
We give a consistent example of a zero-dimensional separable metrizable space Z such that every homeomorphism of Zω 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 ω1 Cohen reals, viewed as a subspace of 2ω .
منابع مشابه
Weak Covering Properties and Infinite Games
We investigate game-theoretic properties of selection principles related to weaker forms of the Menger and Rothberger properties. For appropriate spaces some of these selection principles are characterized in terms of a corresponding game. We use generic extensions by Cohen reals to illustrate the necessity of some of the hypotheses in our theorems.
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