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Author:
Ilijas Farah

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

Published electronically:
October 1, 2001

MathSciNet review:
1873803

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the Cech-Stone remainder of the integers, , 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.

**1.**I. Farah. Dimension phenomena associated with -spaces.*Topology and its Applications*, to appear; available at http://www.math.csi.cuny.edu/farah.**2.**W. Just. The space is not always a continuous image of .*Fundamenta Mathematicae*, 132:59-72, 1989. MR**90h:54013****3.**J. van Mill. A Peano continuum homeomorphic to its own square but not to its countable infinite product.*Proceedings of the American Mathematical Society*, 80:703-705, 1980. MR**81k:54061****4.**J. van Mill. An introduction to . In*Handbook of Set-theoretic topology*(K. Kunen and J. Vaughan, editors), pages 503-560. North-Holland, 1984. MR**86f:54027****5.**I.I. Parovicenko. A universal bicompact of weight .*Soviet Mathematics Doklady*, 4:592-592, 1963.**6.**W. Sierpinski. Remarque sur la courbe péanienne.*Wiadomosci Matematyczne*, 42:1-3, 1937. reproduced in: W. Sierpinski, Oeuvres Choisies, (1976), volume III, p. 369-371. MR**54:2407****7.**S. Solecki. personal communication. September 2000.

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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:
https://doi.org/10.1090/S0002-9939-01-06191-3

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