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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Combinatorial aspects of F$_\sigma$ filters with an application to $\mathcal N$-sets
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by Claude Laflamme
Proc. Amer. Math. Soc. 125 (1997), 3019-3025
DOI: https://doi.org/10.1090/S0002-9939-97-03926-9

Abstract:

We discuss F$_\sigma$ filters and show that the minimum size of a filter base generating an undiagonalizable filter included in some F$_\sigma$ filter is the better known bounded evasion number ${\frak e}_{ubd}$. An application to $\mathcal {N}$-sets from trigonometric series is given by showing that if $A$ is an $\mathcal {N}$-set and $B$ has size less than ${\frak e}_{ubd}$, then $A \cup B$ is again an $\mathcal {N}$-set.
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Bibliographic Information
  • Claude Laflamme
  • Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
  • Email: laflamme@acs.ucalgary.ca
  • Received by editor(s): September 18, 1995
  • Received by editor(s) in revised form: May 1, 1996
  • Additional Notes: This research was partially supported by NSERC of Canada.
  • Communicated by: Andreas R. Blass
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3019-3025
  • MSC (1991): Primary 04A20; Secondary 03E05, 03E15, 03E35
  • DOI: https://doi.org/10.1090/S0002-9939-97-03926-9
  • MathSciNet review: 1401747