Definition:Image/Mapping/Mapping

Definition

Let $f: S \to T$ be a mapping.

The image (or image set) of a mapping $f: S \to T$ is the set:

$\operatorname{Im} \left ({f}\right) = f \left ({S}\right) = \left\{ {t \in T: \exists s \in S: f \left({s}\right) = t}\right\}$

Notes

Some sources refer to this as the direct image of a mapping, in order to differentiate it from an inverse image.

Rather than apply a mapping $f$ directly to a subset $A$, those sources prefer to define the mapping induced by $f$ as a separate concept in its own right.

Also seen is the term image set of mapping for $\operatorname{Im} \left ({f}\right)$.

Also see

• Domain
• Codomain
• Range

• Preimage (also known as an inverse image)

Sources

• Iain T. Adamson: Introduction to Field Theory (1964)... (previous)... (next): $\S 1.3$
• W.E. Deskins: Abstract Algebra (1964): $\S 1.3$
• Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): $\S 11$
• Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 21.1$