Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

This question already has an answer here:

How can I prove that nested sequence of non-empty bounded closed convex sets in Hilbert space have nonempty intersection?

I just don't know where to start.

Thanks

share|improve this question

marked as duplicate by Jonas Meyer, Care Bear, Daniel Fischer, Ivo Terek, Conifold Aug 18 at 3:17

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

4  
Do you know the weak topology for Hilbert space? –  GEdgar Nov 6 '11 at 21:03
    
I don't know what it is. –  Slon Nov 6 '11 at 21:18
3  
What do you know about closed bounded convex sets in a Hilbert space, then? –  t.b. Nov 6 '11 at 21:48
1  
Proof without weak topology is here. –  Care Bear Aug 17 at 22:15

1 Answer 1

This is Cantors Intersection Theorem. The (simple) proof can be found here for example. You need to use the fact that closed bounded convex subsets in a Hilbert space H are weakly compact.

share|improve this answer
3  
Unfortunately, if he doesn't know what is the weak topology, he probably also doesn't know anything about "weakly compact". This illustrates the standard wisdom: For problems with homework, seek help from the instructor. –  GEdgar Nov 7 '11 at 1:40

Not the answer you're looking for? Browse other questions tagged or ask your own question.