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Commit 2021-12-09 05:38 11bf7e52

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feat(analysis/normed_space/weak_dual): add polar sets in preparation for Banach-Alaoglu theorem (#9836) The first of two parts to add the Banach-Alaoglu theorem about the compactness of the closed unit ball (and more generally polar sets of neighborhoods of the origin) of the dual of a normed space in the weak-star topology. This first half is about polar sets (for a set s in a normed space E, the polar s is the subset of weak_dual _ E consisting of the functionals that evaluate to something of norm at most one at all elements of s).

Estimated changes

added def polar
added theorem polar_closed_ball
added theorem polar_empty
added theorem polar_eq_Inter
added theorem smul_mem_polar
added theorem zero_mem_polar