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

 

Powers of $\mathbb N^*$


Author: Ilijas Farah
Journal: Proc. Amer. Math. Soc. 130 (2002), 1243-1246
MSC (2000): Primary 54B10, 54D30, 54D35, 54C05
Published electronically: October 1, 2001
MathSciNet review: 1873803
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Abstract: We prove that the Cech-Stone remainder of the integers, $\mathbb N^*$, maps onto its square if and only if there is a nontrivial map between two of its different powers, finite or infinite. We also prove that every compact space that maps onto its own square maps onto its own countable infinite product.


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Additional Information

Ilijas Farah
Affiliation: Department of Mathematics, College of Staten Island, 2800 Victory Blvd., Staten Island, New York 10314 and Mathematical Institute, Kneza Mihaila 35, 11000 Beograd, Yugoslavia
Email: ifarah@gc.cuny.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06191-3
PII: S 0002-9939(01)06191-3
Keywords: \v Cech-Stone compactifications, product spaces, continuous images
Received by editor(s): August 10, 2000
Received by editor(s) in revised form: October 31, 2000
Published electronically: October 1, 2001
Additional Notes: The author acknowledges support received from the National Science Foundation (USA) via grant DMS-0070798 and from the PSC-CUNY grant
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society