December 1st, 2009, 06:44 AM  #1 
Newbie Joined: Aug 2009 Posts: 29 Thanks: 0  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? 
December 1st, 2009, 07:00 AM  #2 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  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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convergence, uniform 
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