Hi guys,

The question I'm doing states,

"Let be indices in , and assume that for each , we are given . Show that can be described as a product of subsets of 's"

I just want to see if my thinking here is correct.

We have that is given by the projection onto the ith factor. So, , for instance. We have the following fact for some ,

where

Now, I know I have to use this to prove the above question, I'm just stuck on how I would represent using the above, and how to then manipulate the intersections. There is a further property that

,

which perhaps may come in useful, although I haven't seen any use for it.

Thanks in advance,

HTale.