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Results in Mathematics

, 73:114 | Cite as

Continuous Projections onto Ideal Convergent Sequences

  • Paolo Leonetti
Article

Abstract

Let \({\mathcal {I}}\subseteq \mathcal {P}(\omega )\) be a meager ideal. Then there are no continuous projections from \(\ell _\infty \) onto the set of bounded sequences which are \({\mathcal {I}}\)-convergent to 0. In particular, it follows that the set of bounded sequences statistically convergent to 0 is not isomorphic to \(\ell _\infty \).

Keywords

Meager ideal \({\mathcal {I}}\)-maximal almost disjoint family complementability asymptotic density zero sets \({\mathcal {I}}\)-convergent sequence 

Mathematics Subject Classification

Primary: 40A35 46B03 Secondary: 54A20 46B26 

Notes

Acknowledgements

The author is grateful to Tommaso Russo (Università degli Studi di Milano, IT) for suggesting Question 1 and Lemma 1.1.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of StatisticsUniversità “L. Bocconi”MilanItaly

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