Infinite Powers and Cohen Reals. Issue 4 (1st December 2018)

• Record Type: Journal Article
• Authors: Medini, Andrea; van Mill, Jan; Zdomskyy, Lyubomyr
• Is Part Of: Canadian mathematical bulletin =. Volume 61:Issue 4(2018)
• Page Start: 812
• Page End: 821
• Publication Date: 2018-12-01
• Subjects: 03E35 -- 54B10 -- 54G20; infinite power -- zero-dimensional -- first-countable -- homogeneous -- Cohen real -- rigid -- h-homogeneous; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2017-055-x
• Languages: English
• ISSNs: 0008-4395

Abstract

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