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Ordered Compactifications of Products of Two Totally Ordered Spaces |
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| Authors: | Mooney Douglas D. Richmond Thomas A. |
| Affiliation: | (1) The Center for Healthcare Industry Performance Studies, 1550 Old Henderson Road, Columbus, OH, 43220, U.S.A;(2) Department of Mathematics, Western Kentucky University, Bowling Green, KY, 42101, U.S.A |
| Abstract: | We describe the semilattice of ordered compactifications of X × Y smaller than  oX × oY where X and Y are certain totally ordered topological spaces, and where oZ denotes the Stone– ech ordered- or Nachbin-compactification of Z. These basic cases are used to illustrate techniques for describing the semilattice of ordered compactifications of X × Y smaller than oX × oY for arbitrary totally ordered topological spaces X and Y. Such products X × Y provide many counterexamples in the theory of ordered compactifications. |
| Keywords: | Nachbin compactification ordered compactification semilattice singularity totally ordered topological space |
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