International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 117-124
doi:10.1155/S0161171293000146

A new 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 10 September 1991; Revised 11 April 1992

Copyright © 1993 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.

Abstract

A new Wallman-type ordered compactification γ∘X is constructed using maximal CZ-filters (which have filter bases obtained from increasing and decreasing zero sets) as the underlying set. A necessary and sufficient condition is given for γ∘X to coincide with the Nachbin compactification β∘X; in particular γ∘X=β∘X whenever X has the discrete order. The Wallman ordered compactification ω∘X equals γ∘X whenever X is a subspace of Rn. It is shown that γ∘X is always T1, but can fail to be T1-ordered or T2.