I have this topology on $\mathbb{R}^2$
$\tau=\{\emptyset\}\cup \{\Omega_r, r\geq0\}$ where $\Omega_r=\{(x,y)\in \mathbb{R}^2, (x-2)^2+(y+2)^2\geq r^2\}$
How to find the closure of the center $cl(\{(2,-2)\})$?
The only open which intersect the center is $\Omega_0=\mathbb{R}^2$
how to continue ?
The set $\Bbb R^2\setminus\{(2,-2)\}=\bigcup_{r\gt0}\Omega_r$ is open. Thus $\{(2,-2)\}$ is closed, and is its own closure.