(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find sequences {f_n} {g_n} which converge uniformly on some set E, but such that {f_n*g_n} does not converge uniformly on E.

2. Relevant equations

3. The attempt at a solution

I looked at some sequences of functions known to be convergent but not uniformly convergent and tried to find {f_n} and {g_n} from that. However, I have not enough sequences at hand, I could not find a proper sequence.

I guess it is not the right way to solve this question. But I've no idea how to construct such. Any hint? Thanks

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# Homework Help: A simple question: uniform convergence of sequences

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