316 citations · 1.6k across the 59 of their papers we have counts for
5 papers · 1 filter
Discrete Homology Theory for Metric Spaces
Helene Barcelo, Valerio Capraro, Jacob A. White
In this paper we define and study a notion of discrete homology theory for metric spaces. Instead of working with simplicial homology, our chain complexes are given by Lipschitz ma…
A notion of continuity in discrete spaces and applications
Valerio Capraro
We propose a notion of continuous path for locally finite metric spaces, taking inspiration from the recent development of A-theory for locally finite connected graphs. We use this…
Amenability, locally finite spaces, and bi-lipschitz embeddings
Valerio Capraro
We define the isoperimetric constant for any locally finite metric space and we study the property of having isoperimetric constant equal to zero. This property, called Small Neigh…
Topology on locally finite metric spaces
Valerio Capraro
The necessity of a theory of General Topology and, most of all, of Algebraic Topology on locally finite metric spaces comes from many areas of research in both Applied and Pure Mat…
On the axiomatization of convex subsets of Banach spaces
Valerio Capraro, Tobias Fritz
We prove that any convex-like structure in the sense of Nate Brown is affinely and isometrically isomorphic to a closed convex subset of a Banach space. This answers an open questi…