Maximal Separation Theorems for Convex Sets

摘要

Most previous applications of separation theorems for convex sets have depended on rather crude separation results. Recent developments, however, indicate a need for more refined theorems, particularly for ones involving stronger types of separation. The stronger types of separation considered in this study include nice, open, closed, strict, and strong. The attempt to obtain separation theorems under minimal hypotheses suggests a search for maximal theorems, since each such theorem is, in a sense, a best possible result. Eighteen maximal theorems for disjoint nonempty convex subsets are derived, involving open, nice, strong and strict separation. (Author)