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Published online by Cambridge University Press: 16 December 2021
In this chapter, we introduce the fundamental concepts investigated, namely coarse structures, coarsely bounded sets and large-scale geometry. We show how all topological groups carry an intrinsic coarse structure and determine when this is metrisable. We furthermore discuss quasi-metric structures and spaces and show how, in many familiar cases, the coarse structure on a topological group admits a refinement to a quasi-metric structure.
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