Lineability in sequence and function spaces

We prove the existence of large algebraic structures - including large vector subspaces or infinitely generated free algebras - inside, among others, the family of Lebesgue measurable functions that are surjective in a strong sense, the family of nonconstant differentiable real functions vanishing o...

Full description

Bibliographic Details
Authors: Araujo, G., Bernal-González, L., Muñoz-Fernández, Gustavo A., Prado-Bassas, J. A., Seoane Sepúlveda, Juan Benigno
Format: article
Publication Date:2017
Country:España
Institution:Universidad Complutense de Madrid (UCM)
Repository:Docta Complutense
Language:English
OAI Identifier:oai:docta.ucm.es:20.500.14352/17816
Online Access:https://hdl.handle.net/20.500.14352/17816
Access Level:Open access
Keyword:517.5
517.98
Dense-lineability
Differentiable function
Divergent series
Measurable function
Separate continuity
Análisis funcional y teoría de operadores
Funciones (Matemáticas)
1202 Análisis y Análisis Funcional
Description
Summary:We prove the existence of large algebraic structures - including large vector subspaces or infinitely generated free algebras - inside, among others, the family of Lebesgue measurable functions that are surjective in a strong sense, the family of nonconstant differentiable real functions vanishing on dense sets, and the family of discontinuous separately continuous real functions. Lineability in special spaces of sequences is also investigated.