Consider the following topology on three point set $X$=$\{a,b,c\}$. $\tau=\{X,\emptyset,\{a\},\{a,b\}\}$.
This is clearly a topology on $X$.
Can somebody please explain me how this becomes a $T_0$ space and not a $T_1$ space?
For the two points $a$ and $c$, we have the open set $a$ in $\{a\}$ and $\{c\}$ is not in $\{a\}$. So is $T_0$. but for the two points $a$ and $b$, $a$ in $\{a,b\}$ and $b$ is also in $\{a,b\}$, so isn't $T_0$. But it says that this is $T_0$. How can this be?