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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A non-trivial copy of $ \beta\mathbb{N}\setminus\mathbb{N}$


Author: Alan Dow
Journal: Proc. Amer. Math. Soc. 142 (2014), 2907-2913
MSC (2010): Primary 54A25, 03E35
Published electronically: April 7, 2014
MathSciNet review: 3209343
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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.


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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
Email: adow@uncc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11985-X
PII: S 0002-9939(2014)11985-X
Keywords: Stone-Cech, PFA, homeomorphism
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.