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What are some interesting corollaries and consequences of the Pontryagin Duality theorem? My question can be taken as broadly as you'd like, even up to including any philosophy introduced specifically by the theorem. But of course examples and specific consequences would be most appreciated.

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    Can you give some context, e.g., are you taking a course or reading a book on this topic, are you learning about Pontryagin duality with a particular goal in mind, are you preparing to teach a course where this will be a central concept?2012-10-11

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