Some aspects of dentability in bitopological and locally convex spaces

This paper is a continuation of the study we presented in [6]. A modified v ersion of Namioka's argument is reconsidered to obtain an extended form of a result of Namika-Asplund; this leads to the improvement of several theore ms and to a generalized version of the Dunford Pettis theorem [2]. Moreover , two versions of Rieffel's converse theorem are discussed. It is shown tha t the first one holds true in locally convex spaces, but not generally in t he spaces with two topologies; the second leads to a new characterization o f the Radon-Nikodym property in real Banach spaces and in their duals.