Sierpiński-Zygmund functions and other problems on lineability

Gámez-Merino, José; Muñoz-Fernández, Gustavo; Sánchez, Víctor; Seoane-Sepúlveda, Juan

doi:10.1090/S0002-9939-2010-10420-3

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

Proc. Amer. Math. Soc. 138 (2010), 3863-3876

DOI: https://doi.org/10.1090/S0002-9939-2010-10420-3

Published electronically: May 24, 2010

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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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