Let $T_1$, $T_2$ and $T_3$ be topologies on a set X such that is $T_1⊂ T_2 ⊂ T_3$ and $(X,T_2)$ is a compact Hausdorff space. Then which of the followings are true?
1. $T_1$= $T_2$ if $(X, T_1)$ is a Hausdorff space.
2. $T_1$=$T_2$ if $(X,T_1)$ is a compact space.
3. $T_2$ =$T_3$ if $(X, T_3)$ is a Hausdorff space.
4. $T_2$ = $T_3$ if $(X, T_3)$ is a compact space.
How can I solve this problem.can anybody help me.