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Excursions into combinatorial geometry.

Author: Vladimir Boltyanski; Horst Martini; Petru S Soltan
Publisher: [S.l.] : Springer, 1997.
Series: Universitext
Edition/Format:   Print bookView all editions and formats

Discusses the combinatorial geometry of convex bodies in finite-dimensional spaces. The text includes a general introduction to geometric convexity and investigates d-convexity and H-convexity. Open  Read more...


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Document Type: Book
All Authors / Contributors: Vladimir Boltyanski; Horst Martini; Petru S Soltan
ISBN: 3540613412 9783540613411
OCLC Number: 468744225
Description: 418 p.
Contents: I Convexity1 Convex sets2 Faces and supporting hyperplanes3 Polarity4 Direct sum decompositions5 The lower semicontinuity of the operator 'exp'6 Convex cones7 The Farkas Lemma and its generalization8 Separable Systems of convex cones II d-Convexity in normed spaces 9 The definition of d-convex sets10 Support properties of d-convex sets11 Properties of d-convex flats12 The join of normed spaces13 Separability of d-convex sets14 The Helly dimension of a set family15 d-Star-shaped sets II H-convexity16 The functional md for vector systems17 TheE-displacement Theorem18 Lower semicontinuity of the functional md19 The definition of H-convex-sets20 Upper semicontinuity of H-convex hull21 Supporting cones of H-convex bodies22 The Helly Theorem for H-convex sets23 Some applications of H-convexity24 Some remarks on connection between d-convexity and H-convexity IV The Szokefalvi-Nagy Problem25 The Theorem of Szokefalvi-Nagy and its generalization26 Description of vector systems with md H=2 that are not one-sided27 The 2-systems without particular vectors28 The 2-system wiht particular vectors29 The compact, convex bodies with md M=230 Centrally symmetric bodies V Borsuk's partition problem31 Formulation of the problem and a survey of results32 Bodies of constant width in Euclidean and normed spaces33 Borsuk's problem in normed spaces VI Homothetic covering and illumination34 The main problem and a survey of results35 The hypothesis of Gohberg-Markus-Hadwiger36 The infinite values of the functionals b, b', c, c'37 Inner illumination of convex bodies38 Estimates for the value of the functional p(K) VII Cominatorial geometry of belt bodies39 The integral representation of zonoids40 Beltvectors of a compact, convex body41 Definition of belt bodies42 Solution of the illuminations problem for belt bodies43 Solution of the Szokefalvi-Nagy problem for belt bodies44 Minumal fixing systems VIII Some research problems Bibliography Author Index Subject Index List of Symbols
Series Title: Universitext
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