order bidual. An order complete, regularly ordered vector lattice whose canonical image in its order bidual is order complete is called minimal and is said to be of minimal type. Examples For any , the Banach lattice is order complete and of minimal type; in particular, the norm topology on this space is the finest locally convex topology for which every order convergent filter converges. Properties Let be an order complete vector lattice of minimal type. For any such that the following are equivalent: is a weak order unit. For every non-0 positive linear functional on , For each topology on such that is a locally convex vector lattice, is a quasi-interior point of its positive cone. Related concepts An ordered vector space is called regularly ordered and its order is said to be regular if it is Archimedean ordered and distinguishes points in . See also References Bibliography Functional analysis