Question on compactification

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This is not an exercise from a textbook, but a question regarding a remark in a textbook, so I was not sure if this question belongs here or in the homework section. Forgive me if I have erred.

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.
 

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Well, for anyone who has looked at this thread and might be even remotely interested, I think I have more or less worked it out for myself. The key appears to be to construct the Stone-Cech compactification in terms of ultrafilters. I do not recall ever having done it that way before, so it has been a learning experience. In fact, I did not even begin to catch on to this until I started looking at some of Marshall Stone's original work on the subject.
 

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