MAXIMAL SEPARATION THEOREMS FOR CONVEX SETS,

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)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1967
Accession Number
AD0662331

Entities

People

  • Victor Klee

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Convex Sets
  • Hypotheses
  • Mathematics
  • Theorems

Readers

  • Mathematical Modeling and Probability Theory.
  • Theoretical Analysis.