Tree metrics and their Lipschitz-free spaces

TL;DR

This paper characterizes subsets of metric trees through their Lipschitz-free spaces, showing that these spaces are isometric to subspaces of L1, and computes the Lipschitz-free spaces for subsets of the real line.

Contribution

It provides a characterization of subsets of metric trees via Lipschitz-free spaces and computes these spaces for subsets of the real line.

Findings

Lipschitz-free spaces of subsets of the real line are computed.

Subsets of metric trees are characterized by their Lipschitz-free spaces being isometric to subspaces of L1.

The paper establishes a link between metric tree subsets and L1 subspaces.

Abstract

We compute the Lipschitz-free spaces of subsets of the real line and characterize subsets of metric trees by the fact that their Lipschitz-free space is isometric to a subspace of $L_1$.