  Uniformity and proximity are two different ways for defining small scale
structures on a set. Coarse structures are large scale counterparts of uniform
structures. In this paper, motivated by the definition of proximity, we develop
the concept of asymptotic resemblance as a relation between subsets of a set to
define a large scale structure on it. We use our notion of asymptotic
resemblance to generalize some basic concepts of coarse geometry. We introduce
a large scale compactification which in special cases agrees with Higson
compactification. At the end we show that how the asymptotic dimension of a
metric space can be generalized to a set equipped with an asymptotic
resemblance relation.
