We prove that a continuous image of a Radon-Nikodým compact of weight less than b is Radon-Nikodým compact. As a Banach space counterpart, subspaces of Asplund generated Banach spaces of density character less than b are Asplund generated. In this case, in addition, there exists a subspace of an Asplund generated space which is not Asplund generated which has density character exactly b. The concept of Radon-Nikodým compact, due to Reynov [12], has its origin in Banach space theory, and it is defined as a topological space which is homeomorphic to a weak∗ compact subset of the dual of an Asplund space, that is, a dual Banach space with the Radon-Nikodým property (topological spaces will be here assumed to be Hausdorff). In [9], the following characterization of this class is given: Theorem 1. A compact space K is Radon-Nikodým compact if and only if there is a lower semicontinuous metric d on K which fragments K. Recall that a map f : X ×X −→ R on a topological space X is said to fragment X if for each (closed) subset L of X and each e > 0 there is a nonempty relative open subset U of L of f -diameter less than e, i.e. sup{f(x, y) : x, y ∈ U} < e. Also, a map g : Y −→ R from a topological space to the real line is lower semicontinuous if {y : g(y) ≤ r} is closed in Y for every real number r. It is an open problem whether a continuous image of a Radon-Nikodým compact is Radon-Nikodým. Arvanitakis [2] has made the following approach to this problem: if K is a Radon-Nikodým compact and π : K −→ L is a continuous surjection, then we have a lower semicontinuous fragmenting metric d on K, and if we want to prove that L is Radon-Nikodým compact, we should find such a metric on L. A natural candidate is: d1(x, y) = d(π−1(x), π−1(y)) = inf{d(t, s) : π(t) = x, π(s) = y}. The map d1 is lower semicontinuous and fragments L and it is a quasi metric, that is, it is symmetric and vanishes only if x = y. But it is not a metric because, in general, it lacks triangle inequality. Consequently, Arvanitakis [2] introduced the 2000 Mathematics Subject Classification. Primary: 46B26. Secondary: 46B22, 46B50, 54G99.