Generalizations of a Theorem of Caratheodory.

Intro -- CONTENTS -- 0. INTRODUCTION -- 1. STANDARD GENERALIZATIONS OF CARATHÉODORY'S THEOREM -- 2. POSITIVE BASES OF LINEAR SPACES -- 2.1 Notation and Fundamental Results -- 2.2 The Partitioning of Positive Bases -- 2.3 Application to Carathéodory Type Theorems -- 3. CARATHÉODORY'S THEOREM WITH CONNECTEDNESS CONDITIONS -- 3.1 The Hnnner-Radström Theorem Extended to Interior Points -- 3.2 Apparently Connected Sets -- 4. CARATHÉODORY!S THEOREM WITH AT LEAST TWO POINTS IN con X -- 4.1 An Extension of Bonnice-Klee's Theorem -- 4.2 An Extension with Distinct Constraints -- 5. CARATHÉODORY'S THEOREM WITH SYMMETRY CONDITIONS -- 5.1 Introduction -- 5.2 A Generalization of Fenchel's and Bonnice-Klee's Theorems -- 5.3 Symmetry Theorems With At Least 2 Points In con X -- BIBLIOGRAPHY.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.