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aymane amine

General topology

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Your double negative is a little confusing!  Also, by "(-1/n, 1/n)" so you mean the interval or the pair of numbers.  If the first, what "product topology" are you talking about?  If the latter, that's a single point, not a set.

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I'm guessing they mean the product in the infinite product of the real line. 

 

Have you tried applying the definitions of the two topologies?

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