Duality of Discrete Topological Vector Spaces

Abstract

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

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