TITLE: Example of a uniformly convergent subsequence of a sequence of function which is pointwise convergent.
QUESTION [1 upvotes]: let $ {f_n} $ be a sequence of function on any subset of $ \mathbb R $ and it converges pointwise to zero. Is it possible to get a subsequence which converges uniformly to zero? 
    Thanks in advance.

REPLY [0 votes]: A classic example is the sequence $f_n(x)=x^n, n=1,2,\dots $ on $(0,1).$
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