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Compact subsemigroups of (βℕ, +) containing the idempotents

Published online by Cambridge University Press:  20 January 2009

Neil Hindman  and
Dona Strauss
Neil Hindman
Affiliation:
Department of Mathematics Howard University Washington D.C. 20059, U.S.A.
Dona Strauss
Affiliation:
Department of Pure Mathematics University of Hull Cottingham Road Hull HU6 7RX
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Abstract

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The space βℕ is the Stone-Čech compactification of the discrete space of positive integers. The set of elements of βℕ which are in the kernel of every continuous homomorpnism from βℕ to a topological group is a compact semigroup containing the idempotents. At first glance it would seem a good candidate for the smallest such semigroup. We produce an infinite nested sequence of smaller such semigroups all defined naturally in terms of addition on ℕ.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 2 , June 1996 , pp. 291 - 307
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

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