The Katowice problem and autohomeomorphisms of ω0⁎

David Chodounský; Alan Dow; Klaas Pieter Hart; Harm de Vries

doi:10.1016/j.topol.2016.08.006

The Katowice problem and autohomeomorphisms of ω0⁎

David Chodounský, Alan Dow, Klaas Pieter Hart, Harm de Vries

Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

3 Citations (Scopus)

Abstract

We show that the existence of a homeomorphism between ω0⁎ and ω1⁎ entails the existence of a non-trivial autohomeomorphism of ω0⁎. This answers Problem 441 in [8]. We also discuss the joint consistency of various consequences of ω0⁎ and ω1⁎ being homeomorphic.

Original language	English
Pages (from-to)	230-237
Number of pages	8
Journal	Topology and Its Applications: a journal devoted to general, geometric, set-theoretic and algebraic topology
Volume	213
DOIs	https://doi.org/10.1016/j.topol.2016.08.006
Publication status	Published - 2016

Keywords

Katowice problem
Homeomorphism
Non-trivial autohomeomorphism
Čech–Stone remainder
ω0⁎
ω1⁎
Isomorphism
Non-trivial automorphism
Quotient algebra
P(ω0)/fin
P(ω1)/fin

Access to Document

10.1016/j.topol.2016.08.006

Cite this

@article{e3b354c763ff4995ba05f34691fe2da9,

title = "The Katowice problem and autohomeomorphisms of ω0⁎",

abstract = "We show that the existence of a homeomorphism between ω0⁎ and ω1⁎ entails the existence of a non-trivial autohomeomorphism of ω0⁎. This answers Problem 441 in [8]. We also discuss the joint consistency of various consequences of ω0⁎ and ω1⁎ being homeomorphic.",

keywords = "Katowice problem, Homeomorphism, Non-trivial autohomeomorphism, {\v C}ech–Stone remainder, ω0⁎, ω1⁎, Isomorphism, Non-trivial automorphism, Quotient algebra, P(ω0)/fin, P(ω1)/fin",

author = "David Chodounsk{\'y} and Alan Dow and Hart, {Klaas Pieter} and {de Vries}, Harm",

year = "2016",

doi = "10.1016/j.topol.2016.08.006",

language = "English",

volume = "213",

pages = "230--237",

journal = "Topology and Its Applications: a journal devoted to general, geometric, set-theoretic and algebraic topology",

issn = "0166-8641",

publisher = "Elsevier",

}

TY - JOUR

T1 - The Katowice problem and autohomeomorphisms of ω0⁎

AU - Chodounský, David

AU - Dow, Alan

AU - Hart, Klaas Pieter

AU - de Vries, Harm

PY - 2016

Y1 - 2016

N2 - We show that the existence of a homeomorphism between ω0⁎ and ω1⁎ entails the existence of a non-trivial autohomeomorphism of ω0⁎. This answers Problem 441 in [8]. We also discuss the joint consistency of various consequences of ω0⁎ and ω1⁎ being homeomorphic.

AB - We show that the existence of a homeomorphism between ω0⁎ and ω1⁎ entails the existence of a non-trivial autohomeomorphism of ω0⁎. This answers Problem 441 in [8]. We also discuss the joint consistency of various consequences of ω0⁎ and ω1⁎ being homeomorphic.

KW - Katowice problem

KW - Homeomorphism

KW - Non-trivial autohomeomorphism

KW - Čech–Stone remainder

KW - ω0⁎

KW - ω1⁎

KW - Isomorphism

KW - Non-trivial automorphism

KW - Quotient algebra

KW - P(ω0)/fin

KW - P(ω1)/fin

U2 - 10.1016/j.topol.2016.08.006

DO - 10.1016/j.topol.2016.08.006

M3 - Article

SN - 0166-8641

VL - 213

SP - 230

EP - 237

JO - Topology and Its Applications: a journal devoted to general, geometric, set-theoretic and algebraic topology

JF - Topology and Its Applications: a journal devoted to general, geometric, set-theoretic and algebraic topology

ER -

The Katowice problem and autohomeomorphisms of ω0⁎

Abstract

Keywords

Access to Document

Fingerprint

Cite this