Small subsets of asymptotic resemblance spaces and their Higson corona (Q6545485)

The author defines small subsets of asymptotic resemblance spaces and obtains some of their properties. He shows that if the ideal of all small subsets of a metric space \(X\) coincides with the ideal of all bounded subsets of \(X\), then the asymptotic dimension of \(X\) is equal to zero. He also shows that a subset \(A\) of a proper metric space \(X\) is small, if and only if, the interior of the boundary of \(A\) in the Higson corona of \(X\) is empty.