Infinite pointwise lineability: general criteria and applications

Abstract

In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set of infinite differentiable and integrable functions, for any order $p \geq 1$, on $\mathbb{R}^N$ which are unbounded in a prefixed set.