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I want to know example of a sequence of function $\{f_n\}$ where each $f_n$ is continuous and the pointwise limit $f$ is continuous, but $f_n$ is not uniformly convergent. clearly, I need to think for a $f_n$ where there exist an $x$ such that $f_n(x)$ is not monotone.

user103623
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    or even nicer: http://math.stackexchange.com/questions/405644/does-pointwise-convergence-against-a-continuous-function-imply-uniform-convergen – BIS HD Nov 29 '13 at 11:41

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