Combination Theorem for Continuous Functions/Product Rule

Theorem

Real Functions

Let $f$ and $g$ be real functions which are continuous on an open subset $S \subseteq \R$.

$f g$ is continuous on $S$

Complex Functions

Let $f$ and $g$ be complex functions which are continuous on an open subset $S \subseteq \C$.

$f g$ is continuous on $S$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): continuous function (continuous mapping)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): continuous function (continuous mapping, continuous map)