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math.GN2019
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…
math.GN2019
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…
math.GN2019
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…