Lineability in the sets of Baire and continuous real functions

Abstract

Discovering large algebraic structures within various sets of exotic real-valued (or complex-valued) functions or sequences is a very active research program now. For a cardinal number η a subset A of a vector space X is said to be η-lineable if there is a vector subspace Z⊂X of dimension η with Z⊂A∪{0}. In this article, we investigate lineability properties in certain vector spaces of Baire-two functions and continuous real-valued functions.