This award will support collaborative research in modern analysis between Dr. Isaac Namioka, Department of Mathematics, University of Washington and Drs. C.A. Rogers and J.E. Jayne, University College London, U.K. The research topic proposed is "Properties like the Radon-Nikodym Property." Dr. Namioka is a leading investigator in this area of mathematical research, and Drs. Roger and Jane are also internationally recognized experts in descriptive topology. A compact Hausdorff space is called Radon-Nikodym compact if it is homeomorphic to a weak compact subset of a dual Banach space with the Radon-Nikodym property. Although there are some open questions, the class of Radon-Nikodym compact spaces is reasonably well understood. This cooperative research proposal aims to undertake a similar study for non-compact spaces. During the past year, the three investigators of the proposed project have laid a foundation for the study of topological spaces with Radon-Nikodym type properties. They now propose to develop their theory further and to solve those problems that have arisen in connection with the application of the general theory to specific spaces such as Banach spaces with the weak topology. The results of this research are likely to lead to interesting applications of descriptive set theory to the geometric-measure theoretical structure of Banach spaces.
