When do products distribute over colimits in Top?

In a recent paper, Lawson and Xu give a new class of posets on which the Scott topology of the (poset) product of two posets coincides with the product topology (of each poset with its Scott topology). I will explain that more in detail next month. The following question is at the heart of their approach, and this is what I will focus on this month. Given two diagrams F and G in Top, we can form their colimits colim F and colim G. We can also consider the product diagram F × G. Is it true that colim (F × G) = colim F × colim G? We will see that this is rarely the case—I will give counterexamples—and that one of the most general situations where that is actually true is given by what I will call ω-rigid diagrams of core-compact spaces. Read the full post.