Geodesic
A metrizable completely regular ordered space
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 4, pp. 773-778.

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We construct a completely regular ordered space $(X,{\Cal T},\leq)$ such that $X$ is an $I$-space, the topology $\Cal T$ of $X$ is metrizable and the bitopological space $(X,{\Cal T}^\sharp,{\Cal T}^{\flat})$ is pairwise regular, but not pairwise completely regular. (Here ${\Cal T}^\sharp$ denotes the upper topology and ${\Cal T}^\flat$ the lower topology of $X$.)
Classification : 06F30, 54E15, 54E55, 54F05
Keywords: completely regular ordered; strictly completely regular ordered; pairwise completely regular; pairwise regular; $I$-space 
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     title = {A metrizable completely regular ordered space},
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Künzi, Hans-Peter A.; Watson, Stephen. A metrizable completely regular ordered space. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 4, pp. 773-778. http://geodesic.mathdoc.fr/item/CMUC_1994__35_4_a17/