ON HAUSDORFF COMPACTIFICATIONS OF NON-LOCALLY COMPACT SPACES

Let X be a completely regular, Hausdorff space and let R be the set of points in X which do not possess compact neighborhoods. Assume R is compact. If X has a compactification with a countable remainder, then so does the quotient X/R, and a countable compactificatlon of X/R implies one for X-R. A characterization of when X/R has a compactification with a countable remainder is obtained. Examples show that the above implications