Let S1, S2 be nonempty sets in a normed linear space. Whatever the nature of the set
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Whatever the nature of the set S, S* and S** are always cones (in X* and X respectively) and S S**. Under what conditions is S identical to its bipolar S** (rather than a proper subset)? Clearly, a necessary condition is that S is a convex cone. The additional requirement is that S is closed. This is another implication of the strong separation theorem.
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SI s S2 = S; s S
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