# Composite of Continuous Mappings is Continuous/Corollary

< Composite of Continuous Mappings is Continuous(Redirected from Continuity of Composite Mapping/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

These follow directly from:

$\blacksquare$

## Sources

- 1953: Walter Rudin:
*Principles of Mathematical Analysis*... (next): $4.7$