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International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 2, Pages 209-221
doi:10.1155/S0161171290000321

Separation properties of the Wallman ordered compactification

D. C. Kent1 and T. A. Richmond2

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 Hindawi Publishing Corporation. 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

The Wallman ordered compactification ω0X of a topological ordered space X is T2-ordered (and hence equivalent to the Stone-Čech ordered compactification) iff X is a T4-ordered c-space. In particular, these two ordered compactifications are equivalent when X is n dimensional Euclidean space iff n≤2. When X is a c-space, ω0X is T1-ordered; we give conditions on X under which the converse statement is also true. We also find conditions on X which are necessary and sufficient for ω0X to be T2. Several examples provide further insight into the separation properties of ω0X.