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David J. Fernández Bretón
Every strongly summable ultrafilter on ⊕Z2 is sparse view print
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| Published: |
March 23, 2013 |
| Keywords: |
ultrafilters, Stone-Čech compactification, sparse ultrafilter, strongly summable ultrafilter, finite sums, Boolean group, abelian group. |
| Subject: |
03E75 (Primary); 54D35, 54D80 (Secondary). |
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Abstract
We investigate the possibility of the existence of nonsparse strongly summable ultrafilters on certain abelian
groups. In particular, we show that every strongly summable ultrafilter on the countably infinite Boolean group is
sparse. This answers a question of Hindman, Steprans and Strauss.
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| Acknowledgements
The author would like to thank the support received from the Consejo Nacional de Ciencia y Tecnología (CONACyT), Mexico, by means of scholarship number 213921/309058.
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| Author information
Department of Mathematics and Statistics, York University, 4700 Keele St., Toronto, Ontario, Canada, M3J 1P3.
davidfb@mathstat.yorku.ca
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