How to prove that the set of extreme points of $B_{\ell^1} = \{v \in \ell^1 : \| v \| \le 1\}$ is $\{ +e^N, -e^N : N=1,2,3,\ldots \}$, where $e^N$ denotes the Nth standard basis element in $\ell_1$: $e_n^N=0$ if $n\neq N$ and $e_N^N =1$.
Also, is $B_{\ell^1}$ the norm closure of the convex hull of its set of extreme points? How to prove this? I don't know how to do it. Please help.