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

Indecomposable continua as Higson coronae