Permanence results for dimension-theoretic coarse notions

Coarse topology is the study of interesting topological properties of discrete spaces. In this dissertation, we will discuss a coarse analog of dimension and several generalizations. We begin by extending the class of metric spaces for which these properties are known. The next few chapters are devoted to generalizing these properties to all coarse spaces and exploring the relationships between these generalizations. Finally, we give a brief discussion of computational topology, highlighting how to generate the Rips and Cech simplicial complexes from a set of data. We end with some code written to generate these complexes, and present some thoughts on how to use this to compute certain coarse properties