Strong algebrability of sets of sequences and functions

Bartoszewicz, Artur; Gła̧b, Szymon

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

Strong algebrability of sets of sequences and functions
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by Artur Bartoszewicz and Szymon Gła̧b PDF

Proc. Amer. Math. Soc. 141 (2013), 827-835 Request permission

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.

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