  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.
