International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1990 / Article

Open Access

Volume 13 |Article ID 714926 | https://doi.org/10.1155/S0161171290000321

D. C. Kent, T. A. Richmond, "Separation properties of the Wallman ordered compactification", International Journal of Mathematics and Mathematical Sciences, vol. 13, Article ID 714926, 13 pages, 1990. https://doi.org/10.1155/S0161171290000321

Separation properties of the Wallman ordered compactification

Received19 Dec 1988
Revised08 Feb 1990

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 n2. 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.

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.


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