Infinite powers and Cohen reals

Andrea Medini; Jan van Mill; Lyubomyr Zdomskyy

doi:10.4153/CMB-2017-055-x

Infinite powers and Cohen reals

Andrea Medini
, Jan van Mill
, Lyubomyr Zdomskyy

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We give a consistent example of a zero-dimensional separable metrizable space Z such that every homeomorphism of Z ^ω 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 ω ₁ Cohen reals, viewed as a subspace of 2 ^ω

Original language	English
Pages (from-to)	812-821
Number of pages	10
Journal	Canadian Mathematical Bulletin
Volume	61
Issue number	4
Early online date	2017
DOIs	https://doi.org/10.4153/CMB-2017-055-x
Publication status	Published - Dec 2018

Austrian Fields of Science 2012

101013 Mathematical logic
101022 Topology

Keywords

Cohen real
first-countable
h-homogeneous
homogeneous
infinite power
rigid
zero-dimensional
Homogeneous
Infinite power
Zero-dimensional
First-countable
H-homogeneous
Rigid

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10.4153/CMB-2017-055-x

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title = "Infinite powers and Cohen reals",

abstract = "We give a consistent example of a zero-dimensional separable metrizable space Z such that every homeomorphism of Z ω 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 ω 1 Cohen reals, viewed as a subspace of 2 ω ",

keywords = "Cohen real, first-countable, h-homogeneous, homogeneous, infinite power, rigid, zero-dimensional, Homogeneous, Infinite power, Zero-dimensional, First-countable, H-homogeneous, Rigid",

author = "Andrea Medini and \{van Mill\}, Jan and Lyubomyr Zdomskyy",

note = "Publisher Copyright: {\textcopyright} Canadian Mathematical Society 2017.",

year = "2018",

month = dec,

doi = "10.4153/CMB-2017-055-x",

language = "English",

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T1 - Infinite powers and Cohen reals

AU - Medini, Andrea

AU - van Mill, Jan

AU - Zdomskyy, Lyubomyr

N1 - Publisher Copyright: © Canadian Mathematical Society 2017.

PY - 2018/12

Y1 - 2018/12

N2 - We give a consistent example of a zero-dimensional separable metrizable space Z such that every homeomorphism of Z ω 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 ω 1 Cohen reals, viewed as a subspace of 2 ω

AB - We give a consistent example of a zero-dimensional separable metrizable space Z such that every homeomorphism of Z ω 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 ω 1 Cohen reals, viewed as a subspace of 2 ω

KW - Cohen real

KW - first-countable

KW - h-homogeneous

KW - homogeneous

KW - infinite power

KW - rigid

KW - zero-dimensional

KW - Homogeneous

KW - Infinite power

KW - Zero-dimensional

KW - First-countable

KW - H-homogeneous

KW - Rigid

UR - https://www.scopus.com/pages/publications/85052942658

U2 - 10.4153/CMB-2017-055-x

DO - 10.4153/CMB-2017-055-x

M3 - Article

SN - 0008-4395

VL - 61

SP - 812

EP - 821

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

IS - 4

ER -

Infinite powers and Cohen reals

Abstract

Austrian Fields of Science 2012

Keywords

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