16 citations · 30 across the 13 of their papers we have counts for
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Relating asymptotic dimension to Ponomarev's cofinal dimension via coarse proximities
Jeremy Siegert
In this paper we show that the asymptotic dimension of an unbounded proper metric space is bounded above by a coarse analog of Ponomarev's cofinal dimension of topological spaces,…
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…
Coarse Proximity and Proximity at Infinity
Pawel Grzegrzolka, Jeremy Siegert
We define coarse proximity structures, which are an analog of small-scale proximity spaces in the large-scale context. We show that metric spaces induce coarse proximity structures…