Almost maximal topologies on semigroups
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- by Yevhen Zelenyuk PDF
- Proc. Amer. Math. Soc. 139 (2011), 2257-2270 Request permission
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.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2257-2270
- MSC (2010): Primary 22A05, 54G05; Secondary 22A30, 54H11
- DOI: https://doi.org/10.1090/S0002-9939-2010-10738-4
- MathSciNet review: 2775403