# Nested sequence of sets in Hilbert space

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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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
What do you know about closed bounded convex sets in a Hilbert space, then? –  t.b. Nov 6 '11 at 21:48