Ordered separation axioms and the Wallman orderedcompactification

摘要

Two constructions have been given previously of the Wallman orderedcompactification ω_0X of a T_1-ordered, convex ordered topological space(X, τ, ≤).Bothof those papers note that ω_0X is T_1,but need not be T_1-ordered. Using this as onemotivation, we propose a new version of Ti-ordered, called Tr-ordered, which has theproperty that the Wallman ordered compactification of a T_1~K-ordered topological spaceis Tr-ordered. We also discuss the Ro-ordered (R_0~K-ordered) property, defined so thatan ordered topological space is Ti-ordered (T_1~K-ordered) if and only if it is To-orderedand R_0-ordered (R_0~K -ordered).