Category:Combination Theorem for Bounded Continuous Real-Valued Functions

This category contains pages concerning Combination Theorem for Bounded Continuous Real-Valued Functions:

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

Let $\R$ denote the real number line.

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

Let $\lambda \in \R$.

Then the following results hold.

Sum Rule

$f + g$ is a bounded coninuous real-valued function

Negation Rule

$-f$ is a bounded continuous real-valued function

Difference Rule

$f - g$ is a bounded coninuous real-valued function

Product Rule

$f g$ is a bounded continuous real-valued function

Multiple Rule

$\lambda f$ is a bounded continuous real-valued function

Absolute Value Rule

$\size f$ is a bounded continuous real-valued function

Maximum Rule

$f \vee g$ is a bounded continuous real-valued function

Minimum Rule

$f \wedge g$ is a bounded continuous real-valued function