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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