TY  - BOOK
AU  - Vel,M.L.J.Van de
TI  - Theory of convex structures
T2  - North-Holland mathematical library
SN  - 9780080933108 (electronic bk.)
AV  - QA639.5 .V45 1993eb
U1  - 516/.08 22
PY  - 1993///
CY  - Amsterdam, New York
PB  - North-Holland
KW  - Convex domains
KW  - MATHEMATICS
KW  - Geometry
KW  - General
KW  - bisacsh
KW  - fast
KW  - Ensembles convexes
KW  - ram
KW  - Electronic books
N1  - Includes bibliographical references (pages 507-528) and index
N2  - 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
UR  - http://www.sciencedirect.com/science/book/9780444815057
ER  -