Subpower Higson corona of a metric space

We define a subpower Higson corona of a metric space. This corona turns out to be an intermediate corona between the Higson corona and sublinear Higson corona. It is proved that the subpower compactification of an unbounded proper metric space contains a topological copy of the Stone-Čech compactification of a countable discrete space. We also provide an example of a map between geodesic spaces that is not asymptotically Lipschitz but that generates a continuous map of the corresponding subpower Higson coronas.