Q:

Discrete Topology unit disk/unit ball

Let $Y$= {$a,b$} be equipped with the discrete Topology.  Show that the unit disk 
$\mathbb{D}$= {$y\in Y$ | $d(y,a) \le 1$} is not the closure of the open unit ball 
$B_1 (a)$ = {$y\in Y$ | $d(y,a) < 1$}. 
I understand how to word out the interior and closure generally, but I don't even know where to start with this case! 

A:

$B_1(a)=\{a\}$ which has itself as a closure while $\mathbb{D} = Y$ which is not equal to $\{a\}$.

