Radon-Nikodým compact spaces of low weight and Banach spaces

Abstract

We prove that a continuous image of a Radon-Nikodým compact space 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.