Some aspects of dentability in bitopological and locally convex spaces (Q1806237)

If the triple \((E,r_0,r)\) is a bitopological real locally convex Hausdorff space, with the topology \(r\) weaker than the topology \(r_0\), then the author shows that each \(r\)-weak compact convex set, bounded and separable in the space \((E,r_0)\) is \(r\)-dentable. Many interesting results, sometimes stronger versions of known results, are deduced as immediate corollaries of this result. The author also considers the problem of the converse of Rieffel's theorem in the set up of locally convex spaces.