TITLE: Is $C([0,1])$ a compact space?
QUESTION [5 upvotes]: Is $C([0,1])$ (I guesss with the max-norm) a compact space?
I have to know that because I want to apply Arzela Ascoli.

REPLY [4 votes]: No it is not, but you don't need $\rm C([0,1])$ to be compact to apply Ascoli-Arzela, but that $[0,1]$ is compact !