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A metrizable completely regular ordered space

Hans-Peter A. Künzi, Stephen W. Watson (1994)

Commentationes Mathematicae Universitatis Carolinae

We construct a completely regular ordered space $(X, 𝒯, \leq)$ such that $X$ is an $I$ -space, the topology $𝒯$ of $X$ is metrizable and the bitopological space $(X, 𝒯^{♯}, 𝒯^{♭})$ is pairwise regular, but not pairwise completely regular. (Here $𝒯^{♯}$ denotes the upper topology and $𝒯^{♭}$ the lower topology of $X$ .)