Continuous Bijection from Compact to Hausdorff is Homeomorphism/Corollary

Corollary to Continuous Bijection from Compact to Hausdorff is Homeomorphism
Let $T_1$ be a compact space.

Let $T_2$ be a Hausdorff space.

Let $f: T_1 \to T_2$ be a continuous injection.

Then $f$ determines a homeomorphism from $T_1$ to $f \left({T_1}\right)$.

That is, $f$ is an embedding of $T_1$ into $T_2$.

Proof
Follows from Continuous Bijection from Compact to Hausdorff is Homeomorphism and Continuity of Composite with Inclusion.