Excursions into combinatorial geometry:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 418 S. graph. Darst. |
| ISBN: | 3540613412 |
Staff View
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| 245 | 1 | 0 | |a Excursions into combinatorial geometry |c Vladimir Boltyanski ; Horst Martini ; Petru S. Soltan |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
I. Convexity 1
§1 Convex sets 1
§2 Faces and supporting hyperplanes 6
§3 Polarity 12
§4 Direct sum decompositions 15
§5 The lower semicontinuity of the operator exp 20
§6 Convex cones 27
§7 The Farkas Lemma and its generalization 36
§8 Separable systems of convex cones 41
II. d Convexity in normed spaces 49
§9 The definition of d convex sets 49
§10 Support properties of d convex sets 58
§11 Properties of d convex flats 65
§12 The join of normed spaces 74
§13 Separability of d convex sets 81
§14 The Helly dimension of a set family 91
§15 d Star shaped sets 99
III. if convexity 109
§16 The functional md for vector systems 109
§17 The e displacement Theorem 115
§18 Lower semicontinuity of the functional md 121
§19 The definition of // convex sets 125
§20 Upper semicontinuity of the if convex hull 127
§21 Supporting cones of H convex bodies 135
§22 The Helly Theorem for H convex sets 143
§23 Some applications of H convexity 149
§24 Some remarks on connection between d convexity
and // convexity 154
IV. The Szokefalvi Nagy Problem 163
§25 The Theorem of Szokefalvi Nagy and its generalization .... 163
X Table of Contents
§26 Description of vector systems with md H = 2
that are not one sided 173
§27 The 2 systems without particular vectors 177
§28 The 2 system with particular vectors 184
§29 The compact, convex bodies with md M — 1 188
§30 Centrally symmetric bodies 198
V. Borsuk s partition problem 209
§31 Formulation of the problem and a survey of results 209
§32 Bodies of constant width in Euclidean and normed spaces. . 227
§33 Borsuk s problem in normed spaces 239
VI. Homothetic covering and illumination 255
§34 The main problem and a survey of results 255
§35 The hypothesis of Gohberg Markus Hadwiger 275
§36 The infinite values of the functional b,b ,c,c 288
§37 Inner illumination of convex bodies 301
§38 Estimates for the value of the functional p(K) 309
VII. Combinatorial geometry of belt bodies 319
§39 The integral respresentation of zonoids 319
§40 Belt vectors of a compact, convex body 327
§41 Definition of belt bodies 333
§42 Solution of the illumination problem for belt bodies 339
§43 Solution of the Szokefalvi Nagy problem for belt bodies.... 346
§44 Minimal fixing systems 352
VIII. Some research problems 365
Bibliography 393
Author Index 411
Subject Index 415
List of Symbols 419
|
| any_adam_object | 1 |
| author | Boltjanskij, Vladimir G. 1925-2019 Martini, Horst Soltan, Petru S. |
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| dewey-full | 516.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.13 |
| dewey-search | 516.13 |
| dewey-sort | 3516.13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:02:25Z |
| institution | BVB |
| isbn | 3540613412 |
| language | English |
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| physical | X, 418 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
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| series2 | Universitext |
| spelling | Boltjanskij, Vladimir G. 1925-2019 Verfasser (DE-588)122968050 aut Excursions into combinatorial geometry Vladimir Boltyanski ; Horst Martini ; Petru S. Soltan Berlin [u.a.] Springer 1997 X, 418 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Kombinatorische Geometrie - Konvexer Körper Kombinatorische Geometrie (DE-588)4140733-7 gnd rswk-swf Kombinatorische Geometrie (DE-588)4140733-7 s DE-604 Martini, Horst Verfasser aut Soltan, Petru S. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007365364&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boltjanskij, Vladimir G. 1925-2019 Martini, Horst Soltan, Petru S. Excursions into combinatorial geometry Kombinatorische Geometrie - Konvexer Körper Kombinatorische Geometrie (DE-588)4140733-7 gnd |
| subject_GND | (DE-588)4140733-7 |
| title | Excursions into combinatorial geometry |
| title_auth | Excursions into combinatorial geometry |
| title_exact_search | Excursions into combinatorial geometry |
| title_full | Excursions into combinatorial geometry Vladimir Boltyanski ; Horst Martini ; Petru S. Soltan |
| title_fullStr | Excursions into combinatorial geometry Vladimir Boltyanski ; Horst Martini ; Petru S. Soltan |
| title_full_unstemmed | Excursions into combinatorial geometry Vladimir Boltyanski ; Horst Martini ; Petru S. Soltan |
| title_short | Excursions into combinatorial geometry |
| title_sort | excursions into combinatorial geometry |
| topic | Kombinatorische Geometrie - Konvexer Körper Kombinatorische Geometrie (DE-588)4140733-7 gnd |
| topic_facet | Kombinatorische Geometrie - Konvexer Körper Kombinatorische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007365364&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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