I want to understand this proof of the fact that $c$ and $c_0$ aren't isometrically isomorphic, but I have very little experience in working with extremal points.
So how can I verify that the unit ball in $c_0$ didn't have one of these points? I tried to manipulate a generic sequence to obtain two difference sequences but the fact that I have to use a convex combination gives me problems.
And how can i prove that the extremal points are preserved via isometry?
Thanks in advance