Compactifications with Discrete Remainders

Conditions are obtained which characterize when a space has a Hausdorff compactification with a discrete remainder. A characterization is also given for when the minimal perfect compactification of a 0-space has a discrete remainder. It is shown that a metric space has a compactification with a discrete remainder if and only if it is rimcompact. In general, however, for a space to have a compactification with a discrete remainder, it is not necessary that the space be rimcompact.