X is a projective variety, W is a quasi-projective variety over the algebraically closed field k.
I would like to construct a k-algebra isomorphism between O(XxW) and O(W) (the rings of regular functions).
On the level of varieties I know that the projection XxW->W maps closed sets to closed sets. I feel like this should lead me to the algebra, but I have no idea how I would define the map going the other way.