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I gave Pontryagin duality for torsion abelian groups its own entry, cross-linked of course with the examples-section at Pontryagin dual and with all other relevant entries.
Mainly I wanted to record this diagram here in a way that one could link to it quasi-directly:
$\array{ &\mathbb{Z}[p^{-1}]/\mathbb{Z} &\hookrightarrow& \mathbb{Q}/\mathbb{Z} &\hookrightarrow& \mathbb{R}/\mathbb{Z} \\ {}^{\mathllap{hom(-,\mathbb{R}/\mathbb{Z})}}\downarrow \\ &\mathbb{Z}_p &\leftarrow& \hat \mathbb{Z} &\leftarrow& \mathbb{Z} }$I notice that none of the three references currently given at Pontryagin duality for torsion abelian groups really seem to substantiate the main claims made in the entry, and only
provides any relevant details at all.
Maybe there is a more focused reference on the entry’s topic?
for when the editing functionality is back:
A good reference is instead:
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