Strong algebrability of sets of sequences and functions

Authors:
Artur Bartoszewicz and Szymon Głab

Journal:
Proc. Amer. Math. Soc. **141** (2013), 827-835

MSC (2010):
Primary 15A03; Secondary 28A20, 46J10

Published electronically:
July 20, 2012

MathSciNet review:
3003676

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Abstract | References | Similar Articles | Additional Information

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 which are not summable with any power is densely strongly -algebrable. The set of all sequences in whose sets of limit points are homeomorphic to the Cantor set is comeager and strongly -algebrable. The set of all non-measurable functions from is -algebrable. These results complete several by other authors, within the modern context of lineability.

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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 Głab**

Affiliation:
Institute of Mathematics, Technical University of Łódź, Wólczańska 215, 93-005 Łódź, Poland

Email:
szymon.glab@p.lodz.pl

DOI:
http://dx.doi.org/10.1090/S0002-9939-2012-11377-2

Keywords:
Algebrability,
non-summable sequences,
non-measurable functions,
Banach-Mazur game,
accumulation points,
Cantor sets

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

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.