I gave it another stab (I’m trying to see if I can synthesize your feedback without copying you word-for-word as a comprehension test); please feel free to PM me if it still doesn’t look right. I definitely appreciate the assistance tuning my technical writing, and I think it’s likely this will be helpful to future readers.
Maybe something like: an element of ∏i∈IXi is just a way of assigning to each index i∈I an element of the corresponding space Xi?
I gave it another stab (I’m trying to see if I can synthesize your feedback without copying you word-for-word as a comprehension test); please feel free to PM me if it still doesn’t look right. I definitely appreciate the assistance tuning my technical writing, and I think it’s likely this will be helpful to future readers.
Looks good now.