6 papers · 1 filter
Tilings and coverings by balls in
Carlo Alberto De Bernardi, Tommaso Russo, Şeyda Sezgek +1
A famous result of Klee from 1981 is that the Banach space admits a disjoint tiling by balls of radius , for all cardinals with . Klee also observed that…
Extending quasiconvex functions from uniformly convex sets
Carlo Alberto De Bernardi, Libor Veselý
Let be a normed space of a finite dimension at least two, and a closed convex set with nonempty interior. We are interested in extending Lipschitz quasiconvex f…
Packings in classical Banach spaces
Carlo Alberto De Bernardi, Tommaso Russo, Şeyda Sezgek +1
We obtain several new results on the simultaneous packing and covering constant of a Banach space , and its lattice counterpart . Th…
Lattice tilings of Hilbert spaces
Carlo Alberto De Bernardi, Tommaso Russo, Jacopo Somaglia
We construct a bounded and symmetric convex body in (for certain cardinals ) whose translates yield a tiling of . This answers a question due to Fonf and…
Some remarks on almost locally uniformly rotund points
Carlo Alberto De Bernardi, Jacopo Somaglia
We study the relations between different notions of almost locally uniformly rotund points that appear in literature. We show that every non-reflexive Banach space admits an equiva…
A note on point-finite coverings by balls
Carlo Alberto De Bernardi
We provide an elementary proof of a result by V.P.~Fonf and C.~Zanco on point-finite coverings of separable Hilbert spaces. Indeed, by using a variation of the famous argument intr…