Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-29T21:47:38.239Z Has data issue: false hasContentIssue false
  • English
  • Français

Complete Erdős space is unstable

Published online by Cambridge University Press:  07 September 2004

JAN J. DIJKSTRA ,
JAN VAN MILL  and
JURIS STEPRĀNS
JAN J. DIJKSTRA
Affiliation:
Faculteit der Exacte Wetenschappen/Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands. e-mail: dijkstra@cs.vu.nlvanmill@cs.vu.nl
JAN VAN MILL
Affiliation:
Faculteit der Exacte Wetenschappen/Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands. e-mail: dijkstra@cs.vu.nlvanmill@cs.vu.nl
JURIS STEPRĀNS
Affiliation:
Department of Mathematics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3. e-mail: steprans@yorku.ca
Get access Rights & Permissions [Opens in a new window]

Abstract

It is proved that the countably infinite power of complete Erdős space $\Ec$ is not homeomorphic to $\Ec$. The method by which this result is obtained consists of showing that $\Ec$ does not contain arbitrarily small closed subsets that are one-dimensional at every point. This observation also produces solutions to several problems that were posed by Aarts, Kawamura, Oversteegen and Tymchatyn. In addition, we show that the original (rational) Erdős space does contain arbitrarily small closed sets that are one-dimensional at every point.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 137 , Issue 2 , September 2004 , pp. 465 - 473
Copyright
2004 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)