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Elements of finite order in Stone-Čech compactifications

Published online by Cambridge University Press:  20 January 2009

John Baker
Affiliation:
Department of Pure MathematicsUniversity of SheffieldSheffield S3 7RH, England
Neil Hindman
Affiliation:
Department of MathematicsHoward UniversityWashington DC 20059, USA
John Pym
Affiliation:
Department of Pure MathematicsUniversity of SheffieldSheffield S3 7RH, England
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Abstract

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Let S be a free semigroup (on any set of generators). When S is given the discrete topology, its Stone-Čech compactification has a natural semigroup structure. We give two results about elements p of finite order in βS. The first is that any continuous homomorphism of βS into any compact group must send p to the identity. The second shows that natural extensions, to elements of finite order, of relationships between idempotents and sequences with distinct finite sums, do not hold.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

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