# The bipolar theorem from functional analysis

I am referring to this source: http://www.math.unl.edu/~s-bbockel1/929/node6.html.

How can I show the other bipolar theorem where the polar of a prepolar is the closed convex balanced hull? Is it even true?

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 Ah. I have figured out that the real right thing to say for the case given in those notes is "closed convex balanced hull with respect to the weak topology." It's just that this doesn't matter since the weak topology on an NVS has the same closed convex subsets as the norm topology, and the same linear functionals. But if I use that, then I can draw the analogy with the case I want, which uses weak-*. – Jeff Jul 14 '12 at 17:05