Definition:Surjection/Definition 2

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

$f: S \to T$ is a surjection :
 * $f \sqbrk S = T$

or, in the language and notation of direct image mappings:
 * $\map {f^\to} S = T$

That is, $f$ is a surjection its image equals its codomain:
 * $\Img f = \Cdm f$

Also see

 * Equivalence of Definitions of Surjection