A non-trivial copy of $\beta \mathbb N\setminus \mathbb N$
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Abstract:
There is a copy $K$ of the Stone-Cech remainder, $\beta \mathbb N\setminus \mathbb N = \mathbb N^*$, of the integers inside $\mathbb N^*$ that is not equal to $\overline {D}\setminus D$ for any countable discrete $D\subset \beta \mathbb N$. Such a copy of $\mathbb N^*$ is known as a non-trivial copy of $\mathbb N^*$. This answers a longstanding open problem of Eric van Douwen.References
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Additional Information
- Alan Dow
- Affiliation: Department of Mathematics, University of North Carolina-Charlotte, 9201 University City Boulevard, Charlotte, North Carolina 28223-0001
- MR Author ID: 59480
- Email: adow@uncc.edu
- Received by editor(s): June 25, 2012
- Received by editor(s) in revised form: August 17, 2012
- Published electronically: April 7, 2014
- Additional Notes: The author acknowledges support provided by NSF grant DMS-0103985.
- Communicated by: Julia Knight
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 2907-2913
- MSC (2010): Primary 54A25, 03E35
- DOI: https://doi.org/10.1090/S0002-9939-2014-11985-X
- MathSciNet review: 3209343