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

[Cratylus]

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