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December 1st, 2009, 06:44 AM   #1
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Uniform Convergence

Construct a sequence of functions on [0,1] each of which is discontinuous at every point of [0,1] and which converges uniformly to a function that is continuous at every point.

Can anyone help?
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December 1st, 2009, 07:00 AM   #2
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Re: Uniform Convergence

I would try to construct a sequence which converges to constant 0 or 1. There are only so many "good" examples of nowhere continuous functions. Can you find a way to play with one?
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