Lipschitz-free spaces over non-porous subsets of ${\mathbb{R}}^n$

Abstract

We prove that the Lipschitz-free space $\mathcal{F}(M)$ contains a complemented copy of $\mathcal{F}({\mathbb{Z}}^n)$ whenever $M\subset {\mathbb{R}}^n$ is not porous. Consequently, if $M\subset {\mathbb{R}}^n$ is uniformly discrete and not porous then $\mathcal{F}(M)$ is isomorphic to $\mathcal{F}({\mathbb{Z}}^n)$.