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arXiv · 1304.6848

Additivity and lineability in vector spaces

Artur Bartoszewicz·Szymon Gł\cab
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Abstract

G\'amez-Merino, Munoz-Fern\'andez and Seoane-Sep\'ulveda proved that if additivity $\mathcal A(\mathcal F)>\mathfrak c$, then $\mathcal F$ is $\mathcal A(\mathcal F)$-lineable where $\mathcal F\subseteq\mathbb R^\mathbb R$. They asked if $\mathcal A(\mathcal F)>\mathfrak c$ can be weakened. We answer this question in negative. Moreover, we introduce and study the notions of homogeneous lineability number and lineability number of subsets of linear spaces.

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Artur Bartoszewicz, Szymon Gł\cab. 2013-04-25. Additivity and lineability in vector spaces. https://doi.org/10.1016/j.laa.2013.06.007

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