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

Staff Emeritus
Gold Member
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.

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