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.
|Uncontrolled Keywords:||Lineability; Additivity; Jones functions|
|Subjects:||Sciences > Mathematics > Mathematical analysis|
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|Deposited On:||29 May 2012 11:37|
|Last Modified:||29 May 2012 11:37|
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