Excursions into Combinatorial Geometry
Springer Berlin (Verlag)
978-3-540-61341-1 (ISBN)
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 Szökefalvi-Nagy Problem.-
25 The Theorem of Szökefalvi-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. Borsuk's partition problem.-
31 Formulation of the problem and a survey of results.-
32 Bodies of constant width in Euclidean and normed spaces.-
33 Borsuk's 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 illumination problem for belt bodies.-
43 Solution of the Szökefalvi-Nagy problem for belt bodies.-
44 Minimal fixing systems.- VIII. Some research problems.- Author Index.- List of Symbols.
Erscheint lt. Verlag | 14.11.1996 |
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Reihe/Serie | Universitext |
Zusatzinfo | XIV, 423 p. 1 illus. |
Verlagsort | Berlin |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 640 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
Schlagworte | belt body • combinatorics • covering problems • d-convexity • Geometrie • Graph • h-convexity • helly dimension • Kombinatorik • Konvexität • SET |
ISBN-10 | 3-540-61341-2 / 3540613412 |
ISBN-13 | 978-3-540-61341-1 / 9783540613411 |
Zustand | Neuware |
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