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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Almost maximal topologies on semigroups


Author: Yevhen Zelenyuk
Journal: Proc. Amer. Math. Soc. 139 (2011), 2257-2270
MSC (2010): Primary 22A05, 54G05; Secondary 22A30, 54H11
Published electronically: November 19, 2010
MathSciNet review: 2775403
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Abstract: A topology on a semigroup is left invariant if left translations are continuous and open. We show that for every infinite cancellative semigroup $ S$ and $ n\in\mathbb{N}$, there is a zero-dimensional Hausdorff left invariant topology on $ S$ with exactly $ n$ nonprincipal ultrafilters converging to the same point, all of them being uniform.


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Additional Information

Yevhen Zelenyuk
Affiliation: School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa
Email: Yevhen.Zelenyuk@wits.ac.za

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10738-4
PII: S 0002-9939(2010)10738-4
Keywords: Almost maximal space, left invariant topology, Stone-Čech compactification, right maximal idempotent, ultrafilter semigroup, projective.
Received by editor(s): January 26, 2010
Received by editor(s) in revised form: June 7, 2010
Published electronically: November 19, 2010
Additional Notes: This work was supported by NRF grant FA2007041200005 and The John Knopfmacher Centre for Applicable Analysis and Number Theory.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.