There are many names for the same objects that is known as the *Arens--Eells spaces*, *transportation cost spaces, free Banach spaces over a (pointed) metric space, *and* Lipschitz-free Banach spaces*.

The last one bothers me a bit. Doesn't the construction *something-free* mean *free of that something*? Think of alcohol-free drinks. The name *free* in Mathematics means free of further relations, so the name means *free of Mr Lipschitz*, who's been quite dead for some time already.

Is it just slopiness or is there are good reason to call these spaces *Lipschitz-free*?