 A subset is said to be order bounded if it is contained in some order interval.An order unit of a preordered vector space is any element "x" such that the set [−"x", "x"] is absorbing.The set of all linear functionals on a preordered vector space "V" that map every order interval into a bounded set is called the order bound dual of "V" and denoted by "V""b" 
If a space is ordered then its order bound dual is a vector subspace of its algebraic dual.