Some ways in which an arbitrary normed space can be partially ordered so that the norm, or at least the topology, is determined by the ordering are discussed. The orderings which are discussed induce either an order unit norm topology or a base norm topology or both, and in this connection vertices and special vertices of unit balls of normed spaces are characterized. It is shown that the unique decomposition property for a base normed space does not imply the similar property for its second dual space. The determining factors for the space of normal linear functionals on an order unit normed Banach dual space \(X^*\) are studied; a class of spaces \(X^*\) is given for which the norm completely determines the normal functionals, and there is also given a class of spaces \(X^*\) for which this is not the case.