Show that each factor of the retract is[imath]\Pi \f_i [/imath]

[Cratylus]

Show that each factor of the retract is [imath]\Pi f_i[/imath]
In order to show [math]f_i :Y \mapsto X_i[/math] is a retract of
[math]\Pi f_i :Y\mapsto X_i[/math] I have to find a continuous map
[math]r_i: \Pi X_i \mapsto X_i[/math] such that [math]r_i\circ \Pi f_i=f_i[/math]
I am stumped on it.I was thinking let if:[math]Y:\mapsto \Pi X_i[/math] f being continuous