International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 2, Pages 209-221
Separation properties of the Wallman ordered compactification
1Department of Pure and Applied Mathematics, Washington State University, Pullman 99164, WA, USA
2Department of Mathematics, Western Kentucky University, Bowling Green 42101, KY, USA
Received 19 December 1988; Revised 8 February 1990
Copyright © 1990 D. C. Kent and T. A. Richmond. 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.
The Wallman ordered compactification of a topological ordered space is -ordered (and hence equivalent to the Stone-Čech ordered compactification) iff is a -ordered -space. In particular, these two ordered compactifications are equivalent when is dimensional Euclidean space iff . When is a -space, is -ordered; we give conditions on under which the converse statement is also true. We also find conditions on which are necessary and sufficient for to be . Several examples provide further insight into the separation properties of .