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Lineability and additivity in R(R).


Gámez Merino, José Luis and Muñoz-Fernández, Gustavo A. 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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