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On Weierstrass' Monsters and lineability

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Jiménez Rodríguez, Pablo and Muñoz-Fernández, Gustavo A. and Seoane-Sepúlveda, Juan B. (2013) On Weierstrass' Monsters and lineability. Bulletin of the Belgian Mathematical Society-Simon Stevin, 20 (4). pp. 577-763. ISSN 1370-1444

Official URL: http://projecteuclid.org/euclid.bbms/1382448181


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Abstract

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.


Item Type:Article
Uncontrolled Keywords:lineability; spaceability; continuous nowhere differentiable function; Weierstrass' Monster
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:24153
Deposited On:09 Jan 2014 12:31
Last Modified:29 Nov 2016 09:07

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