# A hierarchy in the family of real surjective functions

Mar Fenoy-Muñoz; José Luis Gámez-Merino; Gustavo A. Muñoz-Fernández; Eva Sáez-Maestro

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 486-501
- ISSN: 2391-5455

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topMar Fenoy-Muñoz, et al. "A hierarchy in the family of real surjective functions." Open Mathematics 15.1 (2017): 486-501. <http://eudml.org/doc/288129>.

@article{MarFenoy2017,

abstract = {This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The algebraic structure of the sets of surjective functions we show here is studied using the concept of lineability. In the final sections of this work we also reveal unexpected connections between the different degrees of extreme surjectivity given above and other interesting sets of functions such as the space of additive mappings, the class of mappings with a dense graph, the class of Darboux functions and the class of Sierpiński-Zygmund functions in ℝℝ.},

author = {Mar Fenoy-Muñoz, José Luis Gámez-Merino, Gustavo A. Muñoz-Fernández, Eva Sáez-Maestro},

journal = {Open Mathematics},

keywords = {Lineability; Everywhere surjective; Jones function; Sierpiński-Zygmund function; lineability; everywhere surjective},

language = {eng},

number = {1},

pages = {486-501},

title = {A hierarchy in the family of real surjective functions},

url = {http://eudml.org/doc/288129},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Mar Fenoy-Muñoz

AU - José Luis Gámez-Merino

AU - Gustavo A. Muñoz-Fernández

AU - Eva Sáez-Maestro

TI - A hierarchy in the family of real surjective functions

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 486

EP - 501

AB - This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The algebraic structure of the sets of surjective functions we show here is studied using the concept of lineability. In the final sections of this work we also reveal unexpected connections between the different degrees of extreme surjectivity given above and other interesting sets of functions such as the space of additive mappings, the class of mappings with a dense graph, the class of Darboux functions and the class of Sierpiński-Zygmund functions in ℝℝ.

LA - eng

KW - Lineability; Everywhere surjective; Jones function; Sierpiński-Zygmund function; lineability; everywhere surjective

UR - http://eudml.org/doc/288129

ER -

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