Lineability in sequence and function spaces

TL;DR

This paper demonstrates the existence of large algebraic structures within various function and sequence spaces, including Lebesgue measurable surjective functions, nonconstant differentiable functions with dense zeros, and non-continuous separately continuous functions.

Contribution

It establishes new results on lineability, showing large algebraic substructures in diverse function spaces, extending previous research in the area.

Findings

Existence of large algebraic structures in Lebesgue measurable surjective functions

Presence of large vector subspaces in nonconstant differentiable functions with dense zeros

Identification of large algebraic structures in spaces of sequences

Abstract

It is proved the existence of large algebraic structures \break --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 non-continuous separately continuous real functions. Lineability in special spaces of sequences is also investigated. Some of our findings complete or extend a number of results by several authors.