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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…
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…
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…