# 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.