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Coarse Proximity Spaces, Jeremy D. Siegert

Doctoral Dissertations

This work is meant to present the current general landscape of the theory of coarse proximity spaces. It is largely comprised of two parts that are heavily interrelated, the study of boundaries of coarse proximity spaces, and the dimension theory of coarse proximity spaces. Along the way a study of the relationships between coarse proximity spaces and other structures in coarse geometry are explored.

We begin in chapter 2 by going over the necessary preliminary definitions and concepts from the study of small scale proximity spaces as well as coarse geometry. We then quickly proceed to the introduction of coarse …