Coarse compactifications and controlled products
| Autor: | Fukaya, Tomohiro, Oguni, Shin-ichi, Yamauchi, Takamitsu |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 22 pages |
| Databáze: | arXiv |
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