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Topological dimension of the Gromov-Hausdorff and Gromov-Prokhorov spaces
Hiroki Nakajima, Takamitsu Yamauchi, Nicolò Zava
The Gromov-Hausdorff distance is a dissimilarity metric capturing how far two spaces are from being isometric. The Gromov-Prokhorov distance is a similar notion for metric measure…
Coarse structures on locally compact abelian groups
Dmitri Shakhmatov, Takamitsu Yamauchi, Nicolò Zava
Motivated by the study of the large-scale geometry of topological groups, we investigate particular families of subsets of topological groups named group ideals. We compare differe…
Coarse compactifications and controlled products
Tomohiro Fukaya, Shin-ichi Oguni, Takamitsu Yamauchi
We introduce the notion of controlled products on metric spaces as a generalization of Gromov products, and construct boundaries by using controlled products, which we call the Gro…