 there exists some "y" ∈ "X" such that "nx" ≤ "y" for all formula_14) then "x" ≤ 0.A topological vector space (TVS) that is an ordered vector space is necessarily Archimedean if its positive cone is closed.We say that a preordered vector space "X" is regularly ordered and that its order is regular if it is Archimedean ordered and "X"+ distinguishes points in "X".