Geodesic
Lineability in sequence and function spaces
G. Araújo 1   ; L. Bernal-González 2   ; G. A. Muñoz-Fernández 3   ; J. A. Prado-Bassas 2   ; J. B. Seoane-Sepúlveda 4
1 Departamento de Matemática Centro de Ciências e Tecnologia Universidade Estadual da Paraíba Rua Baraúnas 351 Campina Grande-PB, 58.429-500, Brazil
2 Departamento de Análisis Matemático Universidad de Sevilla Apdo. 1160 Avenida Reina Mercedes Sevilla, 41080, Spain
3 Departamento de Análisis Matemático Facultad de Ciencias Matemáticas Plaza de Ciencias 3 Universidad Complutense de Madrid Madrid, 28040, Spain
4 Instituto de Matemática Interdisciplinar (IMI) and Departamento de Análisis Matemático Facultad de Ciencias Matemáticas Plaza de Ciencias 3 Universidad Complutense de Madrid Madrid, 28040, Spain
Studia Mathematica, Tome 237 (2017) no. 2, pp. 119-136 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm8358-10-2016
Keywords: prove existence large algebraic structures including large vector subspaces infinitely generated algebras inside among others family lebesgue measurable functions surjective strong sense family nonconstant differentiable real functions vanishing dense sets family discontinuous separately continuous real functions lineability special spaces sequences investigated

G. Araújo  1   ; L. Bernal-González  2   ; G. A. Muñoz-Fernández  3   ; J. A. Prado-Bassas  2   ; J. B. Seoane-Sepúlveda  4

1 Departamento de Matemática Centro de Ciências e Tecnologia Universidade Estadual da Paraíba Rua Baraúnas 351 Campina Grande-PB, 58.429-500, Brazil
2 Departamento de Análisis Matemático Universidad de Sevilla Apdo. 1160 Avenida Reina Mercedes Sevilla, 41080, Spain
3 Departamento de Análisis Matemático Facultad de Ciencias Matemáticas Plaza de Ciencias 3 Universidad Complutense de Madrid Madrid, 28040, Spain
4 Instituto de Matemática Interdisciplinar (IMI) and Departamento de Análisis Matemático Facultad de Ciencias Matemáticas Plaza de Ciencias 3 Universidad Complutense de Madrid Madrid, 28040, Spain 
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     title = {Lineability in sequence and function spaces},
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G. Araújo; L. Bernal-González; G. A. Muñoz-Fernández; J. A. Prado-Bassas; J. B. Seoane-Sepúlveda. Lineability in sequence and function spaces. Studia Mathematica, Tome 237 (2017) no. 2, pp. 119-136. doi: 10.4064/sm8358-10-2016

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