Composite of Continuous Mappings is Continuous/Corollary

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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:


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$\blacksquare$


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