Bitopologies on totally ordered sets
The authors study the category of so-called ray bispaces, that is, the category whose objects are totally ordered sets with two topologies, each having a subbase of rays and so that the resulting bitopological space is pairwise weakly symmetric, and whose morphisms are the pairwise continuous functions. Among other things, they show that such spaces are (pairwise) monotonically normal, obtain a bitopological version of the Intermediate Value Theorem and give conditions for the equality of the de Groot dual and the ray dual of a ray topology. They also show that a selective ray topology is compact if and only if it is skew compact.
scientific article; zbMATH DE number 1404416