Accession Number : AD0662331

Title :   MAXIMAL SEPARATION THEOREMS FOR CONVEX SETS,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Klee,Victor

Report Date : NOV 1967

Pagination or Media Count : 37

Abstract : 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)

Descriptors :   (*SET THEORY, THEOREMS), CONTROL, FUNCTIONAL ANALYSIS, INEQUALITIES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE