Template:Universal property of the quotient topology/Diagram

[ilmath]\xymatrix{ X \ar[d]_{q} \ar[dr]^{f\circ q} & \\ Y \ar[r]_f & Z }[/ilmath]
In this commutative diagram [ilmath]f[/ilmath] is continuous [ilmath]\iff[/ilmath] [ilmath]f\circ q[/ilmath] is continuous