UID:
almahu_9947367915102882
Format:
1 online resource (556 p.)
ISBN:
1-282-25849-4
,
9786612258497
,
0-08-093310-6
Series Statement:
North-Holland mathematical library ; v. 50
Content:
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 si
Note:
Description based upon print version of record.
,
Front Cover; Theory of Convex Structures; Copyright Page; Introduction; Table of Contents; List of frequent Symbols; Chapter I Abstract Convex Structures; 1. Basic Concepts; 2. The Hull Operator; 3. Half-spaces and Separation; 4. Interval Spaces; 5. Base-point Orders; 6. Modular Spaces; 7. Bryant-Webster Spaces; Chapter II Convex Invariants; 1. Classical Convex Invariants; 2. Invariants and Product Spaces; 3. Invariants in other Constructions; 4. Infinite Combinatorics; 5. Tverberg Numbers; Chapter III Topological Convex Structures; 1. Topology and Convexity on the same Set
,
2. Continuity of the Hull Operator3. Uniform Convex Structures; 4. Top-convex Separation; 5. Intrinsic Topology; Chapter IV Miscellaneous; 1. Embedding Bryant-Webster Spaces into Vector Spaces; 2. Extremality, Pseudo-boundary and Pseudo-interior; 3. Continuous Selection; 4. Dimension Theory; 5. Dimension and Convex Invariants; 6. Fixed Points; Bibliography; Index of Terms
,
English
Additional Edition:
ISBN 0-444-81505-8
Language:
English
