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Topology

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Properties of Surjective and Injective Maps

TOPO-GH1LXZ

Which of the following statements are TRUE?

Select ALL that apply.

A

If $f: X\rightarrow Y$ is injective, then $\forall g: X\rightarrow Z$, $\exists h: Y\rightarrow Z$ such that $h\circ f=g$.

B

If $f: X\rightarrow Y$ is surjective, then $\forall g: X\rightarrow Z$, $\exists h: Y\rightarrow Z$ such that $h\circ f=g$.

C

If $f: X\rightarrow Y$ is injective, then $\forall g: Z\rightarrow Y$, $\exists h: Z\rightarrow X$ such that $f\circ h=g$.

D

If $f: X\rightarrow Y$ is surjective, then $\forall g: Z\rightarrow Y$, $\exists h: Z\rightarrow X$ such that $f\circ h=g$.