Free Spaces over Countable Compact Metric Spaces

TL;DR

This paper proves that for countable compact metric spaces, the associated Lipschitz-free space is isometric to a dual space and possesses the metric approximation property, advancing understanding of their geometric structure.

Contribution

It establishes that Lipschitz-free spaces over countable compact metric spaces are dual spaces and have the metric approximation property, a novel result in this area.

Findings

Lipschitz-free space over countable compact metric space is isometric to a dual space

Such spaces have the metric approximation property

Advances understanding of geometric structure of these spaces

Abstract

We prove that the Lipschitz-free space over a countable compact metric space is isometric to a dual space and has the metric approximation property.