Strong algebrability of sets of sequences and functions

Bartoszewicz, Artur; Głab, Szymon

doi:10.1090/S0002-9939-2012-11377-2

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

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
Posted: July 20, 2012
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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 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.

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