Coarse compactifications and controlled products
Coarse compactifications and controlled products
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粗致密化和受控产品
DOI：
10.1142/s1793525321500102
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发表时间：
2020
影响因子：
0.8
通讯作者：
Takamitsu Yamauchi
中科院分区：
文献类型：
--
作者：
Tomohiro Fukaya;Shin-ichi Oguni;Takamitsu Yamauchi
我们在度量空间上引入受控乘积的概念，作为Gromov乘积的推广，并利用受控乘积构造边界，我们称之为Gromov边界。证明了真度量空间上关于受控乘积的Gromov边界是该空间粗紧化的理想边界。并证明了受控积的所有粗等价类的集合与粗紧化的所有等价类的集合之间存在双射对应。
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.