## Powers of $\mathbb N^*$

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- by Ilijas Farah
- Proc. Amer. Math. Soc.
**130**(2002), 1243-1246 - DOI: https://doi.org/10.1090/S0002-9939-01-06191-3
- Published electronically: October 1, 2001
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## Abstract:

We prove that the Čech-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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## Bibliographic 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
- MR Author ID: 350129
- Email: ifarah@gc.cuny.edu
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**130**(2002), 1243-1246 - MSC (2000): Primary 54B10, 54D30, 54D35, 54C05
- DOI: https://doi.org/10.1090/S0002-9939-01-06191-3
- MathSciNet review: 1873803