16 citations · 30 across the 13 of their papers we have counts for
13 papers
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…
Abbott Dimension, Mathematics Inspired by Flatland
Jeremy Siegert
What is the "right way" to define dimension? Mathematicians working in the early and middle th-century formalized three intuitive definitions of dimension that all turned out t…
Inductive dimensions of coarse proximity spaces
Pawel Grzegrzolka, Jeremy Siegert
In this paper, we generalize Dranishnikov's asymptotic inductive dimension to the setting of coarse proximity spaces. We show that in this more general context, the asymptotic indu…
Some counterexamples in abstract coarse geometry
Pawel Grzegrzolka, Jeremy Siegert
We construct an example of a coarse proximity space that is not induced by any coarse structure. We then show how to "stitch" two coarse proximity spaces with homeomorphic boundari…
Proximity inductive dimension and Brouwer dimension agree on compact Hausdorff spaces
Jeremy Siegert
In this paper we show that the proximity inductive dimension defined by Isbell agrees with the Brouwer dimension originally described by Brouwer on the class of compact Hausdorff s…
Boundaries of coarse proximity spaces and boundaries of compactifications
Pawel Grzegrzolka, Jeremy Siegert
In this paper, we introduce the boundary of a coarse proximity space This boundary is a subset of the boundary of a certain Smirnov compac…
Normality conditions of structures in coarse geometry and an alternative description of coarse proximities
Pawel Grzegrzolka, Jeremy Siegert
We introduce an alternative description of coarse proximities. We define a coarse normality condition for connected coarse spaces and show that this definition agrees with large sc…
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…
Alternative links, homogeneous links, and graphs
Jeremy Siegert
In this paper we review the definitions of homogeneous and alternative links. We also give two new characterizations of an alternative link diagram, one within the context of the e…
Maximum Waring ranks of monomials
Erik Holmes, Paul Plummer, Jeremy Siegert +1
We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring rank less than the generic rank, with a short list of exceptions. We asymptotica…