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) an...

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Bibliographic Details
Main Author: Vel, M. L. J. Van de
Format: eBook
Language:English
Published: Amsterdam North-Holland 1993, 1993
Series:North-Holland mathematical library
Subjects:
Online Access:
Collection: Elsevier eBook collection Mathematics - Collection details see MPG.ReNa
Description
Summary: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
Physical Description:xv, 540 pages illustrations
ISBN:9780080933108
9781282258495
0080933106
1282258494
9786612258497