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