### Description:

A ballean B is a set X endowed with some family
of subsets of X which are called the balls. We postulate the prop-
erties of the family of balls in such a way that a ballean can be
considered as an asymptotic counterpart of a uniform topological
space. Using slow oscillating functions from X to {0, 1}, we define
a zero-dimensional compact space which is called a binary corona
of B. We define a class of binary normal ballean and, for every bal-
lean from this class, give an intrinsic characterization of its binary
corona. The class of binary normal balleans contains all balleans
of graph. We show that a ballean of graph is a projective limit of
some sequence of ˘ Cech-Stone compactifications of discrete spaces.
The obtained results witness that a binary corona of balleans can
be interpreted as a "generalized space of ends" of ballean.