A hierarchy in the family of real surjective functions

作者：Fenoy Munoz Mar; Luis Gamez Merino Jose; Munoz Fernandez Gustavo A^*; Saez Maestro Eva

来源：Open Mathematics, 2017, 15(1): 486-501.

DOI：10.1515/math-2017-0042

• Lineability
• Everywhere surjective
• Jones function
• Sierpinski-Zygmund function

This expository paper focuses on the study of extreme surjective functions in R-R. 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, k-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 Sierpinski-Zygmund functions in R-R.

• 出版日期2017-4-26