Large algebraic structures inside the set of surjective functions

Abstract

In this note we study large linear structures inside the set of Jones functions, which is a {\em highly pathological class} of surjective functions. We show that there exists an infinite dimensional linear space inside this set of functions. Moreover, we show that this linear space is isomorphic to \(\mathbb{R}^\mathbb{R}\), that is, it has the {\em biggest} possible dimension. The result presented in this note is an improvement of several recent results in the topic of {\em lineability}.