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Keywords:
completely regular ordered; strictly completely regular ordered; pairwise completely regular; pairwise regular; $I$-space
completely regular ordered; strictly completely regular ordered; pairwise completely regular; pairwise regular; $I$-space
Summary:
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 $X$.)
References:
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