1 citations · 2 across the 12 of their papers we have counts for
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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…
On curve-flat Lipschitz functions and their linearizations
Gonzalo Flores, Mingu Jung, Gilles Lancien +3
We show that several operator ideals coincide when intersected with the class of linearizations of Lipschitz maps. In particular, we show that the linearization of a…
Non-uniformly continuous nearest point maps
Rubén Medina, Andrés Quilis
We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not unif…
(Almost isometric) local retracts in metric spaces
Andrés Quilis, Abraham Rueda Zoca
We introduce the notion of (almost isometric) local retracts in metric space as a natural non-linear version of the concepts of locally complemented and almost isometric ideals fro…
Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and -points
Christian Cobollo, Daniel Isert, Ginés López-Pérez +6
We prove that there exists an equivalent norm on with the following properties: (1) The unit ball of $(L_\infty[0,1],\Vert\vert\cdot\ver…
On projectional skeletons and the Plichko property in Lipschitz-free Banach spaces
Antonio J. Guirao, Vicente Montesinos, Andrés Quilis
We study projectional skeletons and the Plichko property in Lipschitz-free spaces, relating these concepts to the geometry of the underlying metric space. Specifically, we identify…
Counterexamples in rotundity of norms in Banach spaces
Petr Hájek, Andrés Quilis
We study several classical concepts in the topic of strict convexity of norms in infinite dimensional Banach spaces. Specifically, and in descending order of strength, we deal with…
Renormings preserving local geometry at countably many points in spheres of Banach spaces and applications
Andrés Quilis
We develop tools to produce equivalent norms with specific local geometry around infinitely many points in the sphere of a Banach space via an inductive procedure. We combine this…
On isometric embeddings into the set of strongly norm-attaining Lipschitz functions
Sheldon Dantas, Rubén Medina, Andrés Quilis +1
In this paper, we provide an infinite metric space such that the set $\mbox{SNA}(M)$ of strongly norm-attaining Lipschitz functions does not contain a subspace which is isometr…
A complete metric space without non-trivial separable Lipschitz retracts
Petr Hájek, Andrés Quilis
We construct a complete metric space of cardinality continuum such that every non-singleton closed separable subset of fails to be a Lipschitz retract of . This provides…
Lipschitz retractions and complementation properties of Banach spaces
Petr Hájek, Andrés Quilis
In the present paper we introduce and study the Lipschitz retractional structure of metric spaces. This topic was motivated by the analogous projectional structure of Banach spaces…