Uniform convergence question

1. Jun 10, 2010

Malmstrom

Let $$y_n$$ be a sequence of functions in $$\mathcal{C}([0,1], \mathbb{R})$$
Suppose that every subsequence of $$y_n$$ has a subsequence that converges uniformly. Prove that they all converge to the same limit.

2. Jun 10, 2010

Landau

So, what have you tried?

3. Jun 10, 2010

Malmstrom

This is not an exercise. This is a question that rose solving an exercise. Can't solve it.