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A topological group is a group $G$ together with a topology on the elements of $G$ such that the group operation and group inverse function are both continuous (with respect to the topology).

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Is every closed subgroup of dual group an annihilator?

Let $G$ be a LCA group. It is well-known that to every closed subgroup $H$ of $G$ correspond a closed subgroup in the dual group $\widehat{G}$, namely the annihilator of $H$. My question is this : is …