# Set Theory and Analysis

usually takes place Every Tuesday 10:00 IM, konírna
Chair: Wieslaw Kubis

### Preserved and unpreserved extreme points in Lipschitz-free spaces

##### Ramon J. Aliaga
Universitat Politecnica de Valencia
Tuesday, 26. June 2018 - 10:00 to 12:00
A result will be presented concerning the characterisation of the preserved extreme points of the unit ball of a Lipschitz-free space $\mathcal{F}(X)$ in terms of geometric conditions in the underlying metric space $(X,d)$. Namely, they are the elementary molecules given by pairs of points $(p,q)$ such that the triangle inequality $d(p,q)\leq d(p,r)+d(q,r)$ is uniformly strict for $r$ away from $p,q$. Some situations will be highlighted where all extreme points, or all extreme elementary molecules, are preserved. Finally, the open problem of identifying all extreme points of the unit ball will be reviewed and the particular cases where it has been solved will be summarized.