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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) an...
| Call Number: | Libro Electrónico |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Amsterdam ; New York :
North-Holland,
1993.
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| Series: | North-Holland mathematical library ;
v. 50. |
| Subjects: | |
| Online Access: | Texto completo Texto completo |
| 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. |
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| Physical Description: | 1 online resource (xv, 540 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 507-528) and index. |
| ISBN: | 9780080933108 0080933106 1282258494 9781282258495 9786612258497 6612258497 |