Strong algebrability of sets of sequences and functions
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Abstract:
We introduce a notion of strong algebrability of subsets of linear algebras. Our main results are the following. The set of all sequences from $c_0$ which are not summable with any power is densely strongly $\mathfrak {c}$–algebrable. The set of all sequences in $l^\infty$ whose sets of limit points are homeomorphic to the Cantor set is comeager and strongly $\mathfrak {c}$-algebrable. The set of all non-measurable functions from $\mathbb {R}^{\mathbb {R}}$ is $2^\mathfrak {c}$–algebrable. These results complete several by other authors, within the modern context of lineability.References
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Additional Information
- Artur Bartoszewicz
- Affiliation: Institute of Mathematics, Technical University of Łódź, Wólczańska 215, 93-005 Łódź, Poland
- Email: arturbar@p.lodz.pl
- Szymon Gła̧b
- Affiliation: Institute of Mathematics, Technical University of Łódź, Wólczańska 215, 93-005 Łódź, Poland
- Email: szymon.glab@p.lodz.pl
- Received by editor(s): May 24, 2011
- Received by editor(s) in revised form: July 19, 2011, and July 23, 2011
- Published electronically: July 20, 2012
- Communicated by: Thomas Schlumprecht
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 827-835
- MSC (2010): Primary 15A03; Secondary 28A20, 46J10
- DOI: https://doi.org/10.1090/S0002-9939-2012-11377-2
- MathSciNet review: 3003676