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arXiv · 1810.08720

Coarse compactifications and controlled products

Tomohiro Fukaya·Shin-ichi Oguni·Takamitsu Yamauchi
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Abstract

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 complements the space as a coarse compactification. 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.

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Tomohiro Fukaya, Shin-ichi Oguni, Takamitsu Yamauchi. 2018-10-20. Coarse compactifications and controlled products. https://arxiv.org/abs/1810.08720

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