11 papers
Gromov-Hausdorff distance between chromatic metric pairs and stability of the six-pack
Ondřej Draganov, Sophie Rosenmeier, Nicolò Zava
Chromatic metric pairs consist of a metric space and a coloring function partitioning a subset thereof into various colors. It is a natural extension of the notion of chromatic poi…
Topological dimension of the Gromov-Hausdorff and Gromov-Prokhorov spaces
Hiroki Nakajima, Takamitsu Yamauchi, Nicolò Zava
The Gromov-Hausdorff distance is a dissimilarity metric capturing how far two spaces are from being isometric. The Gromov-Prokhorov distance is a similar notion for metric measure…
Lower Bounding the Gromov--Hausdorff distance in Metric Graphs
Henry Adams, Sushovan Majhi, Fedor Manin +2
Let be a finite, connected metric graph and let be a subset. If is sufficiently dense in , we show that the Gromov--Hausdorff distance matches the Hausdor…
Coarse structures on locally compact abelian groups
Dmitri Shakhmatov, Takamitsu Yamauchi, Nicolò Zava
Motivated by the study of the large-scale geometry of topological groups, we investigate particular families of subsets of topological groups named group ideals. We compare differe…
On the metric spaces of lattices and periodic point sets
Alexey Garber, Žiga Virk, Nicolò Zava
Lattices and periodic point sets are well known objects from discrete geometry. They are also used in crystallography as one of the models of atomic structure of periodic crystals.…
Coarse and bi-Lipschitz embeddability of subspaces of the Gromov-Hausdorff space into Hilbert spaces
Nicolò Zava
In this paper, we discuss the embeddability of subspaces of the Gromov-Hausdorff space, which consists of isometry classes of compact metric spaces endowed with the Gromov-Hausdorf…
Weakly weighted generalised quasi-metric spaces and semilattices
Ilaria Castellano, Anna Giordano Bruno, Nicolò Zava
Motivated by recent applications to entropy theory in dynamical systems, we generalise notions introduced by Matthews and define weakly weighted and componentwisely weakly weighted…
Stability of the q-hyperconvex hull of a quasi-metric space
Nicolò Zava
In this paper, we study the stability of the q-hyperconvex hull of a quasi-metric space, adapting known results for the hyperconvex hull of a metric space. To pursue this goal, we…
Categories of coarse groups: quasi-homomorphisms and functorial coarse structures
Dikran Dikranjan, Nicolò Zava
Coarse geometry is the study of large-scale properties of spaces. In this paper we study group coarse structures (i.e., coarse structures on groups that agree with the algebraic st…
Hyperballeans of groups
D. Dikranjan, I. Protasov, N. Zava
In this paper we define some ballean structure on the power set of a group and, in particular, we study the subballean with support the lattice of all its subgroups. If is a gr…
Generalisations of coarse spaces
Nicolò Zava
Coarse geometry, the branch of topology that studies the global properties of spaces, was originally developed for metric spaces and then Roe introduced coarse structures as a larg…