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For a compact Hausdorff space with a dense set of isolated points, we give a complete description of points of weak
$^{*}$-norm continuity in the dual unit ball of the space of Banach space valued functions that are continuous when the range has the weak topology. As an application we give a complete description of points of weak-norm continuity of the unit ball of the space of vector measures when the underlying Banach space has the Radon-Nikodym property.
