Excursions into Combinatorial Geometry [Paperback]

I. Convexity.- ?1 Convex sets.- ?2 Faces and supporting hyperplanes.- ?3 Polarity.- ?4 Direct sum decompositions.- ?5 The lower semicontinuity of the operator exp.- ?6 Convex cones.- ?7 The Farkas Lemma and its generalization.- ?8 Separable systems of convex cones.- II. d-Convexity in normed spaces.- ?9 The definition of d-convex sets.- ?10 Support properties of d-convex sets.- ?11 Properties of d-convex flats.- ?12 The join of normed spaces.- ?13 Separability of d-convex sets.- ?14 The Helly dimension of a set family.- ?15 d-Star-shaped sets.- III. H-convexity.- ?16 The functional md for vector systems.- ?17 The ?-displacement Theorem.- ?18 Lower semicontinuity of the functional md.- ?19 The definition of H-convex sets.- ?20 Upper semicontinuity of the H-convex hull.- ?21 Supporting cones of H-convex bodies.- ?22 The Helly Theorem for H-convex sets.- ?23 Some applications of H-convexity.- ?24 Some remarks on connection between d-convexity and H-convexity.- IV. The Sz?kefalvi-Nagy Problem.- ?25 The Theorem of Sz?kefalvi-Nagy and its generalization.- ?26 Description of vector systems with md H = 2 that are not one-sided.- ?27 The 2-systems without particular vectors.- ?28 The 2-system with particular vectors.- ?29 The compact, convex bodies with md M = 2.- ?30 Centrally symmetric bodies.- V. Borsuks partition problem.- ?31 Formulation of the problem and a survey of results.- ?32 Bodies of constant width in Euclidean and normed spaces.- ?33 Borsuks problem in normed spaces.- VI. Homothetic covering and illumination.- ?34 The main problem and a survey of results.- ?35 The hypothesis of Gohberg-Markus-Hadwiger.- ?36 The infinite values of the functional b, b2032;, c, c2032;,.- ?37 Inner illumination of convex bodies.- ?38Estimates for the value of the functional p(K).- VII. Combinatorial geometry of belt bodies.- ?39 The integral respresentation of zonoids.- ?40 Belt vectors of a compact, convex body.- ?41 Definition of belt bodies.- ?42 Solution of the illuminationl£¶