Image of Empty Set is Empty Set/Corollary 1
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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 $10.8 \ \text{(a)}$