Separoids, their categories and a Hadwiger-type theorem for transversals

被引：12

作者：

Arocha, JL ^{[1
]}

Bracho, J ^{[1
]}

Montejano, L ^{[1
]}

Oliveros, D ^{[1
]}

Strausz, R ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2002年 / 27卷 / 03期

关键词：

D O I：

10.1007/s00454-001-0075-2

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we study the topology of transversals to a family of convex sets as a subset of a Grassmanian manifold. This topology seems to be ruled by a combinatorial structure which we call a separoid. With these combinatorial objects and the topological notion of virtual transversal we prove a Borsuk-Ulam-type theorem which has as a corollary a generalization of Hadwiger's theorem.

引用

页码：377 / 385

页数：9

共 50 条

[21] Hadwiger-Wills-type higher-dimensional generalizations of Pick's theorem
Kolodziejczyk, K
DISCRETE & COMPUTATIONAL GEOMETRY, 2000, 24 (2-3) : 355 - 364
[22] A Helly-type theorem for hyperplane transversals to well-separated convex sets
Aronov, B
Goodman, JE
Pollack, R
Wenger, R
DISCRETE & COMPUTATIONAL GEOMETRY, 2001, 25 (04) : 507 - 517
[23] A short proof of Hadwiger's characterization theorem
Klain, DA
MATHEMATIKA, 1995, 42 (84) : 329 - 339
[24] A Helly-Type Theorem for Hyperplane Transversals to Well-Separated Convex Sets
B. Aronov
J. E. Goodman
R. Pollack
R. Wenger
Discrete & Computational Geometry, 2001, 25 : 507 - 517
[25] SURFACE-ENERGY IN LIQUIDS AND THE HADWIGER INTEGRAL THEOREM
BLINOWSKI, A
TRZESOWSKI, A
ARCHIVES OF MECHANICS, 1981, 33 (01): : 133 - 146
[26] THE NORMAL FORM THEOREM AROUND POISSON TRANSVERSALS
Frejlich, Pedro
Marcut, Ioan
PACIFIC JOURNAL OF MATHEMATICS, 2017, 287 (02) : 371 - 391
[27] A Simplified Elementary Proof of Hadwiger's Volume Theorem
Beifang Chen
Geometriae Dedicata, 2004, 105 : 107 - 120
[28] Improvements of the theorem of Duchet and Meyniel on Hadwiger's conjecture
Kawarabayashi, K
Plummer, MD
Toft, B
JOURNAL OF COMBINATORIAL THEORY SERIES B, 2005, 95 (01) : 152 - 167
[29] The Hadwiger theorem on convex functions, IV : The Klain approach
Colesanti, Andrea
Ludwig, Monika
Mussnig, Fabian
ADVANCES IN MATHEMATICS, 2023, 413
[30] A simplified elementary proof of Hadwiger's volume theorem?
Chen, BF
GEOMETRIAE DEDICATA, 2004, 105 (01) : 107 - 120

← 1 2 3 4 5 →