  In this paper, we consider spaces whose Higson coronae are indecomposable
continua. We show that for a non-compact proper metric space $X$ which is
coarsely geodesic and has coarse bounded geometry, the Higson corona of $X$ is
an indecomposable continuum if and only if $X$ is coarsely equivalent to the
space of natural numbers. Then we give characterizations of finitely generated
groups that have one or two ends by decomposability/indecomposability of the
components of their Higson coronae. we characterize it as a group whose Higson
corona is a topological sum of two indecomposable continua.
