38 citations · 72 across the 11 of their papers we have counts for
14 papers
The Ball-Covering Property in Lipschitz-Free Spaces
Ramón J. Aliaga, Colin Petitjean, Antonín Procházka +1
We study ball-covering properties in Lipschitz-free spaces. We establish an extension criterion for proving that fails the ball-covering property and apply it to se…
Affine Approximation in Finite Nagata Dimension and Applications to Lipschitz-free spaces
Mingu Jung, Colin Petitjean, Antonín Prochazka +1
We show that if is a metric space of Nagata dimension at most , then there exists an atlas on modeled on such that every Lipschitz map (with val…
Purely 1-unrectifiable metric spaces and locally flat Lipschitz functions
Ramón J. Aliaga, Chris Gartland, Colin Petitjean +1
We characterize compact metric spaces whose locally flat Lipschitz functions separate points uniformly as exactly those that are purely 1-unrectifiable, resolving a problem of Weav…
Compact reduction in Lipschitz free spaces
Ramón J. Aliaga, Camille Noûs, Colin Petitjean +1
We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in Lipschitz-free spaces over g…
On Kalton's interlaced graphs and nonlinear embeddings into dual Banach spaces
Bruno de Mendonça Braga, Gilles Lancien, Colin Petitjean +1
We study the nonlinear embeddability of Banach spaces and the equi-embeddability of the family of Kalton's interlaced graphs into dual spaces. Not…
Supports in Lipschitz-free spaces and applications to extremal structure
Ramón J. Aliaga, Eva Pernecká, Colin Petitjean +1
We show that the class of Lipschitz-free spaces over closed subsets of any complete metric space is closed under arbitrary intersections, improving upon the previously known fi…
On exposed points of Lipschitz free spaces
Colin Petitjean, Antonín Procházka
In this note we prove that a molecule is an exposed point of the unit ball of a Lispchitz free space if and only if the metric segment $[x,…
On the coarse geometry of James spaces
Gilles Lancien, Colin Petitjean, Antonín Procházka
In this note we prove that the Kalton interlaced graphs do not equi-coarsely embed into the James space nor into its dual . It is a particular case of a…
A characterisation of the Daugavet property in spaces of Lipschitz functions
Luis García-Lirola, Antonín Procházka, Abraham Rueda Zoca
We study the Daugavet property in the space of Lipschitz functions for a complete metric space . Namely we show that has the…
A characterisation of octahedrality in Lipschitz-free spaces
Antonín Procházka, Abraham Rueda Zoca
We characterise the octahedrality of Lipschitz-free space norm in terms of a new geometric property of the underlying metric space. We study the metric spaces with and without this…
Szlenk indices of convex hulls
Gilles Lancien, Antonin Procházka, Matias Raja
We study the general measures of non-compactness defined on subsets of a dual Banach space, their associated derivations and their -iterates. We introduce the notions of convexi…
Characterization of metric spaces whose free space is isometric to
Aude Dalet, Pedro L. Kaufmann, Antonín Procházka
We characterize metric spaces whose Lipschitz free space is isometric to . In particular, the Lipschitz free space over an ultrametric space is not isometric to …
Low distortion embeddings between spaces
Antonín Procházka, Luis Sánchez-González
We show that, for each ordinal , the space does not embed into with distortion strictly less than unless .
Low distortion embeddings into Asplund Banach spaces
Antonín Procházka, Luis Sánchez-González
We give a simple example of a countable metric space that does not embed bi-Lipschitz with distortion strictly less than 2 into any Asplund space. Actually, if embeds with…