RT Journal Article
T1 A hierarchy in the family of real surjective functions
A1 Fenoy Muñoz, María Del Mar
A1 Gámez Merino, José Luis
A1 Muñoz Fernández, Gustavo Adolfo
A1 Sáez Maestro, Eva
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.
PB De Gruyter Open Ltd
SN 23915455
YR 2017
FD 2017
LK https://hdl.handle.net/20.500.14352/17867
UL https://hdl.handle.net/20.500.14352/17867
LA eng
NO Ministerio de Educación, Formación Profesional y Deportes (España)
DS Docta Complutense
RD 8 abr 2025