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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

  • 4
    Do you know the weak topology for Hilbert space?2011-11-06
  • 0
    I don't know what it is.2011-11-06
  • 3
    What do you know about closed bounded convex sets in a Hilbert space, then?2011-11-06
  • 1
    Proof without weak topology is [here](http://math.stackexchange.com/q/900981/).2014-08-17

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