A hierarchy in the family of real surjective functions

• Autorzy: Mar Fenoy-Muñoz , José Luis Gámez-Merino , Gustavo A. Muñoz-Fernández , Eva Sáez-Maestro
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Lineability; Everywhere surjective; Jones function; Sierpiński-Zygmund function

Kategorie tematyczne

• 46J10: Banach algebras of continuous functions, function algebras
• 26A27: Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
• 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
• 15A03: Vector spaces, linear dependence, rank

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 486-501

Daty

wydano

2017-01-01

otrzymano

2016-11-29

zaakceptowano

2017-01-25

online

2017-04-26

Twórcy

autor

Mar Fenoy-Muñoz

• Departamento de Estadística e Investigación Operativa, Universidad Complutense de Madrid, 28040 Madrid,

autor

José Luis Gámez-Merino

• Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid,

autor

Gustavo A. Muñoz-Fernández

• Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid,

autor

Eva Sáez-Maestro

• Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid,

Identyfikatory

DOI

10.1515/math-2017-0042