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I was reading Kusraev and Kutateladze, Boolean Valued Analysis. In it, the authors make the remark that the Stone space of a product of a nonempty set, B_a, a in A, of Boolean algebras is the Stone-Cech compactification of the topological sum St(B_a) X {a}, where St(B_a) is the Stone space of each B_a, and the sum is taken over all a in A.

Now, I admit that my topology is rusty, but I am puzzled by this. Can someone point me to a proof of this assertion? I am sure that it is probably some well-known thing that I have forgotten.