Geodesic
On Some Corollaries of a Transversal Theorem
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 6, pp. 107-111.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider theorems which are generalizations of the well-known corollaries of the Helly theorem.
Keywords: convex set, translate, starshaped set
Mots-clés : transversal. 
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V. L. Dolnikov. On Some Corollaries of a Transversal Theorem. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 6, pp. 107-111. http://geodesic.mathdoc.fr/item/MAIS_2012_19_6_a9/

[1] V. L. Dolnikov, “O transversalyakh semeistv vypuklykh mnozhestv”, Issledovaniya po teorii funktsii mnogikh veschestvennykh peremennykh, Yaroslavl, 1981, 30–36 | MR

[2] V. L. Dolnikov, “Obobschennye transversali semeistv mnozhestv v ${\Bbb R}^n$ i svyazi mezhdu teoremami Khelli i Borsuka”, Dokl. AN SSSR, 297:4 (1987), 777–780 | MR

[3] V. L. Dolnikov, “Obobschennye transversali semeistv mnozhestv v ${\Bbb R}^n$ i svyazi mezhdu teoremami Khelli i Borsuka”, Matem. sbornik, 184:2 (1993), 111–132 | MR

[4] G. Khadviger, G. Debrunner, Kombinatornaya geometriya na ploskosti, Nauka, M., 1965

[5] L. Dantser, B. Gryunbaum, V. Kli, Teorema Khelli i ee primeneniya, Mir, M., 1968 | MR

[6] J. Eckhoff, “Helly, Radon, and Carathéodory type theorems”, Handbook of Convex Geometry, eds. P. M. Gruber, J. M. Wills, North-Holland, Amsterdam, 1993 | MR | Zbl

[7] P. Vincensini, “Sur une extension d'un théorem de M. J. Radon sur les ensembles de corps convexes”, Bull. Sci. Math. France, 67 (1939), 113–119 | MR

[8] V. Klee, “The critical set of a convex body”, Americ. J. Math., 75 (1953), 178–188 | MR | Zbl

[9] H. Minkowski, “Allgemeine Lebrzätze über konvexe Polyeder”, Ges. Ab., 2, Berlin, 1911, 103–121

[10] B. Gryunbaum, Etyudy po kombinatornoi geometrii i teorii vypuklykh tel, Nauka, M., 1971 | MR | Zbl