Dual space of exponential vector space

This paper explores the idea of the dual space of an exponential vector space (evs), focusing on its fundamental properties and structural features. Using the simplest topological evs $[0,\infty)$, over the field $\mathbb{K}$ of all real or complex numbers, we develop the general theory of order-functionals which are an analog of a functional-like structure in the evs-setting. The collection of all order-functionals on an evs is called the dual of the evs, whenever this collection is again an evs. We find a necessary and sufficient condition for this collection to be an evs. We compute the dual of some evs and finally present an application of order-functionals.