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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The autohomeomorphism group of the Cech-Stone compactification of the integers


Author: Juris Steprans
Journal: Trans. Amer. Math. Soc. 355 (2003), 4223-4240
MSC (2000): Primary 03E35
Published electronically: June 10, 2003
MathSciNet review: 1990584
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Abstract: It is shown to be consistent that there is a nontrivial autohomeomorphism of $\beta{\mathbb N} \setminus {\mathbb N}$, yet all such autohomeomorphisms are trivial on a dense $P$-ideal. Furthermore, the cardinality of the autohomeomorphism group of $\beta{\mathbb N} \setminus {\mathbb N}$ can be any regular cardinal between $2^{\aleph_0}$ and $2^{2^{\aleph_0}}$. The model used is one due to Velickovic in which, coincidentally, Martin's Axiom also holds.


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Additional Information

Juris Steprans
Affiliation: Department of Mathematics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3
Email: steprans@yorku.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03329-4
PII: S 0002-9947(03)03329-4
Received by editor(s): January 8, 2001
Received by editor(s) in revised form: March 10, 2003
Published electronically: June 10, 2003
Additional Notes: Research for this paper was partially supported by NSERC of Canada.
Article copyright: © Copyright 2003 American Mathematical Society