The autohomeomorphism group of the Cech-Stone compactification of the integers
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- by Juris Steprāns PDF
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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.References
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Additional Information
- Juris Steprāns
- Affiliation: Department of Mathematics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3
- Email: steprans@yorku.ca
- 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.
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 4223-4240
- MSC (2000): Primary 03E35
- DOI: https://doi.org/10.1090/S0002-9947-03-03329-4
- MathSciNet review: 1990584