Image of Singleton under Mapping

Theorem

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

Then the image of an element of $S$ is equal to the image of a singleton containing that element, the singleton being a subset of $S$:

$\forall s \in S: \set {\map f s} = f \sqbrk {\set s}$

Proof

By definition, a mapping is a relation.

Thus Image of Singleton under Relation applies.

$\blacksquare$

Sources

• 1971: Robert H. Kasriel: Undergraduate Topology ... (previous) ... (next): $\S 1.10$: Functions: Remark $10.8 \ \text{(c)}$