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The dual group of a dense subgroup

William Wistar ComfortS. U. RaczkowskiF. Javier Trigos-Arrieta — 2004

Czechoslovak Mathematical Journal

Throughout this abstract, G is a topological Abelian group and G ^ is the space of continuous homomorphisms from G into the circle group 𝕋 in the compact-open topology. A dense subgroup D of G is said to determine G if the (necessarily continuous) surjective isomorphism G ^ D ^ given by h h | D is a homeomorphism, and G is determined if each dense subgroup of G determines G . The principal result in this area, obtained independently by L. Außenhofer and M. J. Chasco, is the following: Every metrizable group is...

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