Analysis – Compactness of the metric space.

Consider the space $ C ([0,1]$ Equipped with the uniform standard.
Find a sequence of functions $ {g_n } $ in $ C ([0,1]$ so that $ overline { {g_n }} $ It's compact, but $ g_n $ It does not converge uniformly.

I'm confused about $ overline { {g_n }} $ and how to prove its compactness

Thank you!