Separation properties of the Wallman ordered compactification

D. C. Kent and T. A. Richmond

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-13

Abstract:

The Wallman ordered compactification ω 0 X of a topological ordered space X is T 2 -ordered (and hence equivalent to the Stone-Čech ordered compactification) iff X is a T 4 -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, ω 0 X is T 1 -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 ω 0 X to be T 2 . Several examples provide further insight into the separation properties of ω 0 X .

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:714926

DOI: 10.1155/S0161171290000321

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