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Powers of $\mathbb N^*$

Author(s): Ilijas Farah
Journal: Proc. Amer. Math. Soc. 130 (2002), 1243-1246.
MSC (2000): Primary 54B10, 54D30, 54D35, 54C05
Posted: 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.

References:

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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: 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
Posted: 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
Copyright of article: Copyright 2001, American Mathematical Society

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