Maximum Rule for Continuous Functions

Theorem
Let $\struct{S, \tau}$ be a topological space.

Let $f, g: S \to \R$ be continuous real-valued functions.

Let $\max \set{f, g}: S \to \R$ denote the pointwise maximum of $f$ and $g$.

Then:
 * $\max \set{f, g}$ is continuous.