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Lineability and algebrability of pathological phenomena in analysis

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García-Pacheco, F.J. and Palmberg, N. and Seoane-Sepúlveda, Juan B. (2007) Lineability and algebrability of pathological phenomena in analysis. Journal of Mathematical Analysis and Applications, 326 (2). pp. 929-939. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X06002745


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Abstract

We show that, in analysis, many pathological phenomena occur more often than one could expect, that is, in a linear or algebraic way. We show this by means of the construction of large algebraic structures (infinite dimensional vector spaces or infinitely generated algebras) enjoying some special or pathological properties.


Item Type:Article
Uncontrolled Keywords:Algebrability; Spaceability; Hamel basis; Taylor expansion; Linear functions; R-linear functions; Dirichlet function; Everywhere surjective functions
Subjects:Sciences > Mathematics > Functions
ID Code:20079
Deposited On:22 Feb 2013 14:28
Last Modified:25 Nov 2016 12:43

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