Hans-Peter A. K\"unzi, Stephen Watson
A metrizable completely regular ordered space

Comment.Math.Univ.Carolinae 35,4 (1994) 773-778.

Abstract: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 $X$.)

Keywords: completely regular ordered, strictly completely regular ordered, pairwise completely regular, pairwise regular, $I$-space
AMS Subject Classification: 06F30, 54F05, 54E15