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Self-similar functions, fractals and algebraic genericity


Authors: D. Cariello, V. V. Fávaro and J. B. Seoane-Sepúlveda
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 15A03, 26A15
DOI: https://doi.org/10.1090/proc/13552
Published electronically: April 4, 2017
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Abstract: We introduce the class of everywhere like functions, which helps us to recover some known classes (such as that of everywhere surjective ones). We also study the algebraic genericity of this new class together with the class of fractal functions.


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D. Cariello
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Plaza de Ciencias 3, Universidad Complutense de Madrid, Madrid, 28040, Spain — and — Faculdade de Matemática, Universidade Federal de Uberlândia, 38.400-902, Uberlândia, Brazil
Email: dcariello@ufu.br

V. V. Fávaro
Affiliation: Faculdade de Matemática, Universidade Federal de Uberlândia, 38.400-902 Uberlândia, Brazil
Email: vvfavaro@gmail.com

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

DOI: https://doi.org/10.1090/proc/13552
Keywords: Lineability, spaceability, everywhere surjective function, fractal, Darboux.
Received by editor(s): August 30, 2016
Received by editor(s) in revised form: October 24, 2016
Published electronically: April 4, 2017
Additional Notes: The first author was supported by CNPq-Brazil Grant 245277/2012-9
The second author was supported by FAPEMIG Grant PPM-00086-14 and CNPq Grants 482515/2013-9, 307517/2014-4
The third author was supported by MTM2015-65825-P
Communicated by: Ken Ono
Article copyright: © Copyright 2017 American Mathematical Society