International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 3, Pages 481-486
doi:10.1155/S0161171279000375
On Hausdorff compactifications of non-locally compact spaces
Department of Mathematics, Moorhead State University, Moorhead 56560, Minnesota, USA
Received 19 December 1978; Revised 2 February 1979
Copyright © 1979 James Hatzenbuhler and Don A. Mattson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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 cannot be reversed.