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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The set of idempotents
in the weakly almost periodic compactification
of the integers is not closed


Authors: B. Bordbar and J. Pym
Journal: Trans. Amer. Math. Soc. 352 (2000), 823-842
MSC (1991): Primary 43A60, 22A15; Secondary 22D05
Published electronically: July 20, 1999
MathSciNet review: 1491855
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper answers negatively the question of whether the sets of idempotents in the weakly almost periodic compactifications of $(\mathbb{N}, +)$ and $(\mathbb{Z} ,+)$ are closed.


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Additional Information

B. Bordbar
Affiliation: Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, England
Email: j.pym@sheffield.ac.uk

J. Pym
Affiliation: Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, England

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02273-4
PII: S 0002-9947(99)02273-4
Keywords: weakly almost periodic, semigroup compactification, idempotent
Received by editor(s): June 16, 1997
Published electronically: July 20, 1999
Article copyright: © Copyright 1999 American Mathematical Society