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Lineability in sequence and function spaces

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Araujo, G. and Bernal-González, L. and Muñoz-Fernández, Gustavo A. and Prado-Bassas, J. A. and Seoane-Sepúlveda, Juan B. (2017) Lineability in sequence and function spaces. Studia Mathematica, 237 (2). pp. 119-136. ISSN 0039-3223

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Official URL: https://arxiv.org/abs/1507.04477


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Abstract

We prove the existence of large algebraic structures - including large vector subspaces or infinitely generated free algebras - inside, among others, the family of Lebesgue measurable functions that are surjective in a strong sense, the family of nonconstant differentiable real functions vanishing on dense sets, and the family of discontinuous separately continuous real functions. Lineability in special spaces of sequences is also investigated.


Item Type:Article
Uncontrolled Keywords:Dense-lineability; Differentiable function; Divergent series; Measurable function; Separate continuity
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
Sciences > Mathematics > Functions
ID Code:42840
Deposited On:22 May 2017 10:02
Last Modified:22 May 2017 14:44

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