Subcontinua of the Higson corona

Let X be a locally compact separable metric space with proper metric d. Let X̄d denote the Higson compactification of X and let νdX denote the corona of X. The main result of this paper is that if A is a σ-compact subset of νdX, then the closure of A in νdX is equivalent to the Stone-Čech compactification of A. This should be compared with the well known fact that, if X is locally compact and σ-compact and A is a Lindelöf subset of βX β X, then the closure of A in βX β X is equivalent to βA.