What happens to the intersection of subsets when the class is empty?

[samkolb]

I'm starting a book on topology and I've come to this come to this confusing statement:

Let A1, A2, ... be subsets of some universal set U.

If the class {A1, A2, ...} is empty, then the intersection of all the Ai is U.


I know that the intersection of empty sets is empty, but I don't quite see how to even think of the intersection of the Ai when {A1, A2, ...} is empty.

Can anyone explain this?

 

[Hurkyl]

What does it mean for a point not to be in the intersection of a class?

Let P be a point. Can you find a set in your class that doesn't contain P?

 

[samkolb]

I think I get it now. If P is not in some Ai, then Ai must exist in {A1, A2, ...}, which is empty.

Thanks.