Surjective

Definition

$\forall y\in Y,\exists x\in X,f(x)=y⟺\mathrm{Cod}(f)=Y$ A function is surjective if every element in the function’s codomain is the Image of at least one element of its Domain

Facts

Surjective function is an example of an Epimorphism

If a function $f:X\to Y$ is surjective, then $\forall U\subset Y,f(f^{-1}(U))=U$