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By R. (-mtau) Butzmann, H. -p. (d-mnhmm, Reviewed Lydia and D. Außenhofer


Continuous and Pontryagin duality of topological groups. (English summary) Topology Proc. 37 (2011), 315–330. Given an abelian topological group (G, τ), the character group G ∧ c endowed with the compactopen topology is again a topological group and it is called the Pontryagin dual of G. Additionally, the continuous dual Γc(G) is also considered. It is the coarsest convergence structure that makes the mapping ω: G × Γ(G) → T, (x, χ) ↦ → χ(x) continuous. The two settings coincide if G is a locally compact abelian group. The authors outline functorial properties such as left-adjoints and (co-)products of both settings, and state under which conditions the dual object determines the original group

Year: 2013
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