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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Sierpiński-Zygmund functions and other problems on lineability
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by José L. Gámez-Merino, Gustavo A. Muñoz-Fernández, Víctor M. Sánchez and Juan B. Seoane-Sepúlveda PDF
Proc. Amer. Math. Soc. 138 (2010), 3863-3876 Request permission

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
  • MR Author ID: 634110
  • 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
  • MR Author ID: 680972
  • Email: jseoane@mat.ucm.es
  • 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$^{\text {th}}$ anniversary
  • Communicated by: Michael T. Lacey
  • © Copyright 2010 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 3863-3876
  • MSC (2010): Primary 15A03, 26A15, 26A27, 46J10
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10420-3
  • MathSciNet review: 2679609