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math.MG2022
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,…
math.MG2022
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…
math.MG2022
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…