Sierpinski-Zygmund functions and other problems on lineability

• Autores: José L. Gámez Merino, Gustavo Adolfo Muñoz Fernández , Víctor Sánchez, Juan Benigno Seoane Sepúlveda
• Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 138, Nº 11, 2010, págs. 3863-3876
• Idioma: inglés
• DOI: 10.1090/s0002-9939-2010-10420-3
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• Resumen

  • 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) Sierpinski-Zygmund functions. The conclusions obtained on (i) and (iii) are improvements of some already known results.