Aliaga, Ramón J.; Nous, Camille; Petitjean, Colin; Prochazka, Antonin(Institute of Mathematics, Polish Academy of Sciences, 2021)
[EN] We prove a general principle satisfied by weakly precompact sets of Lip-schitz-free spaces. By this principle, certain infinite-dimensional phenomena in Lipschitzfree spaces over general metric spaces may be reduced ...
[EN] We show that, for a separable and complete metric space $M$, the Lipschitz-free space $\mathcal{F}(M)$ embeds linearly and almost-isometrically into $\ell_1$ if and only if $M$ is a subset of an $\mathbb{R}$-tree with ...
[EN] We characterize compact metric spaces whose locally flat Lip-schitz functions separate points uniformly as exactly those that are purely 1-unrectifiable, resolving a problem of Weaver. We subsequently use this geometric ...
[EN] We show that the class of Lipschitz-free spaces over closed subsets of any complete metric space M is closed under arbitrary intersections, improving upon the previously known finite-diameter case. This allows us to ...