# Composite of Continuous Mappings is Continuous/Corollary

## Theorem

Let $T_1, T_2, T_3$ be either:

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

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

## Proof

$\blacksquare$