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:

$\blacksquare$