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

Ramón J. Aliaga

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

Functional Analysis 2026-07-31 v1

Authors: Ramón J. Aliaga

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 $\mathcal{F}(\mathbb{Z}^n)$ .

Keywords

Lipschitz-free space non-porous set complemented copy uniformly discrete isomorphism

Cite

@article{arxiv.2607.29655,
  title  = {Lipschitz-free spaces over non-porous subsets of $\mathbb{R}^n$},
  author = {Ramón J. Aliaga},
  journal= {arXiv preprint arXiv:2607.29655},
  year   = {2026}
}