Weak* closures and derived sets for convex sets in dual Banach spaces

The paper is devoted to the convex-set counterpart of the theory of weak* derived sets initiated by Banach and Mazurkiewicz for subspaces. The main result is the following: For every nonreflexive Banach space X and every countable successor ordinal alpha, there exists a convex subset A in X* such that alpha is the least ordinal for which the weak* derived set of order alpha coincides with the weak* closure of A. This result extends the previously known results on weak* derived sets by Ostrovskii (2011) and Silber (2021).