Composite of Continuous Mappings is Continuous/Corollary

Theorem
Let $T_1, T_2, T_3$ each be one of:


 * metric spaces
 * the complex plane
 * the real number line

Let $f: T_1 \to T_2$ and $g: T_2 \to T_3$ be continuous mappings.

Then the composite mapping $g \circ f: T_1 \to T_3$ is continuous.

Proof
These follow directly from:
 * Real Number Line is Metric Space
 * Complex Plane is Metric Space
 * Metric Induces Topology