We know that a convex hull is defined as the intersection of all convex sets containing a given subset of Euclidean space, equivalently as the set of all convex combinations of points in the subset. And the closure of a convex hull is the closed set.
So I have taken a subset $Y$ in $c_0$ as $Y=closure\{co\{x_n : n \in N\}\}$, where $(x_n)$ = $(-1/n, 0 ,..., 1/2, 0,...)$, 1/2 in the n-th place. Here, we can see that $x_n \rightarrow 0$ weakly. I understand that Y is a closed set. My problem is finding out the closed unit ball of $Y$, which I cannot define here. Kindly help me.
Note: closed unit ball of a set $Y$ is defined as $B_Y = \{y \in Y : ||y|| \leq 1\}$