This award will provide support for research in geometry at the University of Oklahoma. It is aimed primarily at introducing graduate students to research in geometry through research in finitely starlike sets. The goal of the research is to obtain Krasnosel'skii numbers for finitely starlike sets, both in the plane and in higher dimensions. There are two basic problems to be considered, each motivated by existing results for starshaped sets. The first concerns the development of Krasnosel'skii - type (Helly - type) theorems which determine whether a set S is finitely starlike, while the second concerns the development of theorems which reveal the measures of the F - stars in S for F any finite subset of S. This is a very basic area of geometric research. It is expected that graduate students working in this area will be prepared for work in many other areas of research as well, building on the fine program in geometry already in place at Oklahoma.
