Let [tex] y_n [/tex] be a sequence of functions in [tex] \mathcal{C}([0,1], \mathbb{R}) [/tex](adsbygoogle = window.adsbygoogle || []).push({});

Suppose that every subsequence of [tex] y_n [/tex] has a subsequence that converges uniformly. Prove that they all converge to the same limit.

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# Uniform convergence question

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