Abelian extensions of topological vector groups |
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Authors: | U. Cattaneo |
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Affiliation: | Institut de Physique, Université de Neuchâtel, CH-2000 Neuchâtel, Switzerland |
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Abstract: | The possibility of endowing an Abelian topological group G with the structure of a topological vector space when a subgroup F of G and the quotient group are topological vector groups is investigated. It is shown that, if F is a real Fréchet group and a complete metrizable real vector group, then G is a complete metrizable real vector group. This result is of particular interest if is finite dimensional or if F is one dimensional and a separable Hilbert group. |
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