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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sierpiński-Zygmund functions and other problems on lineability


Authors: José L. Gámez-Merino, Gustavo A. Muñoz-Fernández, Víctor M. Sánchez and Juan B. Seoane-Sepúlveda
Journal: Proc. Amer. Math. Soc. 138 (2010), 3863-3876
MSC (2010): Primary 15A03, 26A15, 26A27, 46J10
Published electronically: May 24, 2010
MathSciNet review: 2679609
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Abstract: We find large algebraic structures inside the following sets of pathological functions: (i) perfectly everywhere surjective functions, (ii) differentiable functions with almost nowhere continuous derivatives, (iii) differentiable nowhere monotone functions, and (iv) Sierpiński-Zygmund functions. The conclusions obtained on (i) and (iii) are improvements of some already known results.


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Additional Information

José L. Gámez-Merino
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid 28040, Spain
Email: jlgamez@mat.ucm.es

Gustavo A. Muñoz-Fernández
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid 28040, Spain
Email: gustavo_fernandez@mat.ucm.es

Víctor M. Sánchez
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid 28040, Spain
Email: victorms@mat.ucm.es

Juan B. Seoane-Sepúlveda
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid 28040, Spain
Email: jseoane@mat.ucm.es

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10420-3
PII: S 0002-9939(2010)10420-3
Keywords: Lineability, algebrability, everywhere surjective, nowhere monotone, approximately continuous, Pompeiu derivative.
Received by editor(s): September 17, 2009
Received by editor(s) in revised form: February 1, 2010
Published electronically: May 24, 2010
Additional Notes: The first, second and fourth authors were supported by the Spanish Ministry of Science and Innovation, grant MTM2009-07848.
The third author was supported by the Spanish Ministry of Science and Innovation, grant MTM2008-02652.
Dedicated: Dedicated to Professor Richard M. Aron on his 65$^{th}$ anniversary
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2010 American Mathematical Society