Domain of Continuous Injection to Hausdorff Space is Hausdorff

Theorem
Let $T_\alpha = \left({S_\alpha, \tau_\alpha}\right)$ and $T_\beta = \left({S_\beta, \tau_\beta}\right)$ be topological spaces.

Let $f: S_\alpha \to S_\beta$ be a continuous mapping which is an injection.

If $T_\beta$ is a $T_2$ (Hausdorff) space, then $T_\alpha$ is also a $T_2$ (Hausdorff) space.