Weak⁎ derived sets of convex sets in duals of non-reflexive spaces

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We investigate weak⁎ derived sets, that is the sets of weak⁎ limits of bounded nets, of convex subsets of duals of non-reflexive Banach spaces and their possible iterations. We prove that a dual space of any non-reflexive Banach space contains convex subsets of any finite order and a convex subset of order ω+1.