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