Definition 16.1.2 (Ordered Topological Vector Space).label Let $(E, \le)$ be an ordered vector space over $K \in \RC$, and $\topo$ be a vector space topology on $E$, then the triple $(E, \topo, \le)$ is an ordered topological vector space if the positive cone $C = \bracs{x \in E|x \ge 0}$ is closed.