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Lineability and additivity in R(R).


Gámez Merino, José Luis and Muñoz Fernández, Gustavo Adolfo and Seoane Sepúlveda, Juan Benigno (2010) Lineability and additivity in R(R). Journal of Mathematical Analysis and Applications, 369 . pp. 265-272. ISSN 0022-247X

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We give a condition for a family of functions to be lineable by means of its additivity. The novelty presented here is that we solve the lineability problem using a technique that is not constructive, as are most approaches to this problem. We relate the notions of additivity and lineability and use this relation to give a general method to find the lineability of large families of functions. We also study more examples of pathologically behaving functions, in particular, the class of Jones functions, which is a highly pathological subclass of perfectly everywhere surjective functions. We work on the additivity, lineability, and main properties of this class.

Item Type:Article
Uncontrolled Keywords:Lineability; Additivity; Jones functions
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:15406

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