On weakly Radon–Nikodým compact spaces

A compact space is said to be weakly Radon–Nikodým if it is homeomorphic to a weak*-compact subset of the dual of a Banach space not containing an isomorphic copy of ℓ1. In this paper we provide an example of a continuous image of a Radon–Nikodým compact space which is not weakly Radon–Nikodým. Moreover, we define a superclass of the continuous images of weakly Radon–Nikodým compact spaces and study its relation with Corson compacta and weakly Radon–Nikodým compacta.