If $f_{n}(x)$ are continuous functions from [0, 1] to [0, 1], and $f_{n}(x)\rightarrow f(x)$ as $n\rightarrow \infty $, then which of the following statements is true?
- $f_{n}(x)$ converges to $f(x)$ uniformly on [0, 1]
- $f_{n}(x)$ converges to $f(x)$ uniformly on (0, 1)
- $f(x)$ is continuous on [0, 1]
- None of the above
