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A hierarchy in the family of real surjective functions

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Fenoy, Mar and Gámez Merino, José Luis and Muñoz-Fernández, Gustavo A. and Sáez Maestro, Eva (2017) A hierarchy in the family of real surjective functions. Open Mathematics, 15 (1). pp. 486-501. ISSN 23915455

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Official URL: https://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0042/math-2017-0042.xml


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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.


Item Type:Article
Uncontrolled Keywords:Lineability; Everywhere surjective; Jones function; Sierpiński-Zygmund function
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
Sciences > Mathematics > Functions
ID Code:43250
Deposited On:14 Jun 2017 11:04
Last Modified:20 Dec 2017 08:10

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