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Given a metric space $X$, is there a natural way to view the quasi-isometry group $QI(X)$ as a topological group?
Given a metric space $(X,d)$, we define $QI(X)$ as the set of quasi-isometries $f : X \to X$, modulo the equivalence relation
$$
f \sim g \ \ \ \ \text{ if and only if } \ \ \ \sup_{x \in X} \ d(f(x)...
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