Maximal lineability of the set of Continuous Surjections

Abstract

Let $m,n$ be positive integers. In this short note we prove that the set of all continuous and surjective functions from ${\mathbb{R}}^m$ to ${\mathbb{R}}^n$ contains (excluding the 0 function) a $\mathfrak{c}$-dimensional vector space. This result is optimal in terms of dimension.