Image of Empty Set is Empty Set/Corollary 1

Corollary of Image of Empty Set is Empty Set

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

The image of the empty set is the empty set:

$f \sqbrk \O = \O$

Proof

By definition, a mapping is a relation.

Thus Image of Empty Set is Empty Set applies.

$\blacksquare$

Sources

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