|Authors:||Farah, Ilijas||Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Powers of ℕ*||Journal:||Proceedings of the American Mathematical Society||Volume:||130||Issue:||4||First page:||1243||Last page:||1246||Issue Date:||1-Jan-2002||Rank:||M22||ISSN:||0002-9939||DOI:||10.1090/S0002-9939-01-06191-3||Abstract:||
We prove that the Čech-Stone remainder of the integers, 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.
|Keywords:||Čech-Stone compactifications | Continuous images | Product spaces||Publisher:||American Mathematical Society||Project:||National Science Foundation (USA), Grants DMS-0070798 and PSC-CUNY|
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