Titlebook: Join Geometries; A Theory of Convex S Walter Prenowitz,James Jantosciak Textbook 1979 Springer-Verlag New York Inc. 1979 Equivalence.Factor

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Extremal Structure of Convex Sets: Components and Faces,f vertices, edges and faces of a polyhedron. Properties of extremeness are studied, and two types of extreme subset of a convex set, called components and faces, are singled out for special attention. The components and faces of a convex set . are intimately related, since the interior operation con

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Cones and Hypercones,y of their generalization, hypercones. A cone is defined to be a union of a family of rays that have a common endpoint. Cones which are convex, and of these, especially those which are “pointed”, are of most importance. The problem of how convex cones are generated by their rays receives a major sha

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,Exchange Join Geometries—The Theory of Incidence and Dimension,operty of Euclidean geometry: two points determine a line. Join geometries that satisfy the new postulate are called exchange join geometries or exchange geometries. It is in an exchange join geometry, rather than an arbitrary join geometry, that incidence relations among linear spaces can be satisf

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Ordered Join Geometries,: If three distinct points are collinear, then one of the three is between the other two. Join geometries which satisfy the new postulate are called ordered join geometries or ordered geometries. Ordered geometries are exchange geometries studied in the last chapter, but the results there will not b

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