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