Michal Doucha

On the structure of Lipschitz-free spaces

In this note we study the structure of Lipschitz-free Banach spaces. We show that every Lipschitz-free Banach space over an infinite metric space contains a complemented copy of

Lipschitz-Free Spaces Over Ultrametric Spaces

\ell_1

Metrical universality for groups

. This result has many consequences for the structure of Lipschitz-free Banach spaces. Moreover, we give an example of a countable compact metric space

Scott rank of Polish metric spaces

K

Base Tree Property

such that

Universal and homogeneous structures on the Urysohn and Gurarij spaces

F(K)

Metric Scott analysis

is not isomorphic to a subspace of

Metrically universal abelian groups

L_1

Metric topological groups: their metric approximation and metric ultraproducts

and we show that whenever

Non-abelian group structure on the Urysohn space

M