 For every non-0 positive linear functional "f" on "X", "f"("x") > 0.For each topology 𝜏 on "X" such that ("X", 𝜏) is a locally convex vector lattice, "x" is a quasi-interior point of its positive cone.An ordered vector space "X" is called regularly ordered and its order is said to be regular if it is Archimedean ordered and "X"+ distinguishes points in "X".