17 citations · 88 across the 31 of their papers we have counts for
21 papers · 1 filter
Boundaries for geodesic spaces
Jerzy Dydak, Hussain Rashed
For every proper geodesic space we introduce its quasi-geometric boundary with the following properties: 1. Every geodesic ray in converges to a point…
Ends of spaces via linear algebra
Jerzy Dydak, Hussain Rashed
We develop a theory that may be considered as a prequel to the coarse theory. We are viewing ends of spaces as extra points at infinity. In order to discuss behaviour of spaces at…
Mardesic factorization theorem for asymptotic dimension
Jerzy Dydak, Michael Levin, Jeremy Siegert
The main goal of this note is to prove a coarse analogue of Factorization Theorems in Dimension Theory: Let be a coarsely continuous map. Then factors thro…
Coarse structure of ultrametric spaces with applications
Yuankui Ma, Jeremy Siegert, Jerzy Dydak
We show how to decompose all separable ultrametric spaces into a "Lego" combinations of scaled versions of full simplices. To do this we introduce metric resolutions of large scale…
Universal spaces for asymptotic dimension zero
Yuankui Ma, Jeremy Siegert, Jerzy Dydak
Dranishnikov and Zarichnyi constructed a universal space in the coarse category of spaces of bounded geometry of asymptotic dimension . In this paper we construct universal spac…
Ends of large scale groups
Yuankui Ma, Hussain Rashed, Jerzy Dydak
The aim of this paper is to unify the theory of ends of finitely generated groups with that of ends of locally compact, metrizable and connected topological groups. In both theorie…