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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

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    Proof without weak topology is [here](http://math.stackexchange.com/q/900981/).2014-08-17

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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.

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    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.2011-11-07