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oai:docta.ucm.es:20.500.14352/178672024-07-17T16:18:09Zcom_20.500.14352_14col_20.500.14352_15

Fenoy Muñoz, María Del Mar Gámez Merino, José Luis Muñoz Fernández, Gustavo Adolfo Sáez Maestro, Eva 2023-06-17T21:58:26Z 2023-06-17T21:58:26Z 2017 23915455 10.1515/math-2017-0042 https://hdl.handle.net/20.500.14352/17867 https://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0042/math-2017-0042.xml https://www.degruyter.com/ 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. eng https://creativecommons.org/licenses/by-nc-nd/3.0/es/ open access Atribución-NoComercial-SinDerivadas 3.0 España A hierarchy in the family of real surjective functions journal article