Determine the extreme points of the unit balls of $l^\infty$, and $C([0,1])$ for real-valued functions, with the uniform norm. Is $C([0,1])$ the dual of a Banach space?
I've found the extreme points of $C([0,1])$, but I'm not sure if it is the dual or not.
And can anyone help me with finding the extreme points of the unit balls of $l^\infty$?
Thank you.