I know that the topological space of fibered product of schemes is generally distinct to the usual Cartesian product of toplogical spaces of schemes. Then how can we compute the top. sp. of fibered product of sch. explicitly? Is there any systematic procedure that I can do?
Actually this question arises from when I read the Hartshorne's Algebraic Geometry. In section 4 on Chapter2, the example says that the affine line with doubled origin(I may denote it by X) is not separated over the field k. In the explanation of the book, I can see that the top. sp. of the fibered product of two X . However, I cannot understand how to compute it. (If you want the exact statement, see the p.96 of Hartshorne)