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Título:
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On Weierstrass' Monsters and lineability
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Autores:
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Jiménez Rodríguez, Pablo ;
Muñoz-Fernández, Gustavo A. ;
Seoane-Sepúlveda, Juan B.
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Tipo de documento:
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texto impreso
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Editorial:
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Belgian Mathematical Soc Triomphe, 2013-12
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Análisis matemático
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Tipo = Artículo
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Resumen:
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Let E be a topological vector space and let us consider a property P. We say that the subset M of E formed by the vectors in E which satisfy 2 is mu-lineable (for certain cardinal mu, finite or infinite) if M U {0} contains an infinite dimensional linear space of dimension mu. In 1966 V. Gurariy provided a non-constructive proof of the N-0-lineability of the set of Weierstrass' Monsters (continuous nowhere differentiable functions on R). Here we provide the first constructive proof of the c-lineability of this set (where c denotes the continuum). Of course, this result is the best possible in terms of dimension.
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