Additivity and lineability in vector spaces
Gámez-Merino, Munoz-Fernández and Seoane-Sepúlveda 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...
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| creator | Bartoszewicz, Artur Szymon G\l\cab |
| description | Gámez-Merino, Munoz-Fernández and Seoane-Sepúlveda 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. |
| doi_str_mv | 10.48550/arxiv.1304.6848 |
| format | Article |
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| subjects | Mathematics - Rings and Algebras Vector spaces |
| title | Additivity and lineability in vector spaces |
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