Theory Of Convex Structures
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Theory of Convex Structures
Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology.Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.
Convex Structures and Economic Theory
This book consists of an account of the theory of convex sets and its application to several basic problems that originate in economic theory and adjacent subject matter.
Convex Bodies: The Brunn–Minkowski Theory
Author: Rolf Schneider
language: en
Publisher: Cambridge University Press
Release Date: 2014
A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.