A compact Hausdorff space is called Eberlein compact (EC) if it is homeomorphic to a weakly compact subset of a Banach space. A topological space (X,\(\tau)\) is called fragmented by a metric \(\rho\) defined on X if for each nonempty subset \(A\subset X\) and for each \(\epsilon >0\) there exists a \(\tau\)-open subset U of X such that \(A\cap U\neq \emptyset\) and the \(\rho\)-diameter of \(A\cap U\) is less than \(\epsilon\). It turns out that a weakly compact subset of a Banach space is fragmented with respect to the norm. The present paper deals with the dual question. The family of compact Hausdorff spaces homeomorphic to a weak*-compact subset of a dual space is too large to be of interst. For dual spaces with the Radon-Nikodým property (RNP) the situation is different. Among the things the author shows that weak*-compact subsets of a dual Banach space with RNP is norm-fragmented. A compact Hausdorff-space is called RN compact if it is homeomorphic to a norm-fragmented weak*-compact subset of a dual Banach space. The author establishes the following Banach space free criteria for RN-compactness. A compact Hausdorff space is RN compact if and only if it is fragmented by a lower semicontinuous metric on X.