### Impacto

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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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X10002453

## Abstract

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 |
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Uncontrolled Keywords: | Lineability; Additivity; Jones functions |

Subjects: | Sciences > Mathematics > Mathematical analysis |

ID Code: | 15406 |

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Deposited On: | 29 May 2012 09:37 |

Last Modified: | 06 Feb 2014 10:24 |

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