Coarse compactifications and controlled products
Metric Geometry
2018-10-23 v1 General Topology
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.
Cite
@article{arxiv.1810.08720,
title = {Coarse compactifications and controlled products},
author = {Tomohiro Fukaya and Shin-ichi Oguni and Takamitsu Yamauchi},
journal= {arXiv preprint arXiv:1810.08720},
year = {2018}
}
Comments
22 pages