Mapping/Examples/Definite Integral

Example of Mapping

Let $\mathscr C$ be the set of continuous real functions defined on a closed interval $\closedint a b$.

The definite integral is a mapping which associates an element $f \in \mathscr C$ with a real number $\ds \int_a^b \map f x \rd x$.

Sources

• 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 6$: Functions