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Coarse compactifications and controlled products
Journal of Topology and Analysis  (IF0.457),  Pub Date : 2020-11-16, DOI: 10.1142/s1793525321500102
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 Gromov boundaries. It is shown that the Gromov boundary with respect to a controlled product on a proper metric space is the ideal boundary of a coarse compactification of the space. It is also shown that there is a bijective correspondence between the set of all coarse equivalence classes of controlled products and the set of all equivalence classes of coarse compactifications.