Duality of Discrete Topological Vector Spaces

For a field $\text{ef}$, the discrete topological vector spaces over $\text{ef}$ are essentially of the form ${\text{ef}}^{\alpha }$ where $\alpha$ is an ordinal. With additional appropriate properties, they are isomorphic to ${\text{ef}}^{(\beta )}$ where $\beta$ is again an ordinal. Finally, the categories of the vector spaces of the the first and the second type are equivalent.