16 citations · 37 across the 8 of their papers we have counts for
8 papers
Sums of Reciprocals of Generalized Triangular Numbers
Pawel Grzegrzolka, Jeffrey L. Meyer
We compute the sum and the alternating sum of the reciprocals of triangular numbers using two standard methods from calculus: a telescoping series approach and a power series appro…
Asymptotic dimension of fuzzy metric spaces
Pawel Grzegrzolka
In this paper, we define asymptotic dimension of fuzzy metric spaces in the sense of George and Veeramini. We prove that asymptotic dimension is an invariant in the coarse category…
Coproducts of proximity spaces
Pawel Grzegrzolka
In this paper, we introduce coproducts of proximity spaces. After exploring several of their basic properties, we show that given a collection of proximity spaces, the coproduct of…
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…
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…