Boltyanski Vladimir; Martini Horst: On non-onesided M-complete vector systems. In: Acta scientiarum mathematicarum, (74) 1-2. pp. 297-313. (2008)
![[thumbnail of math_074_numb_001_002_297-313.pdf]](http://acta.bibl.u-szeged.hu/style/images/fileicons/part.png) |
Cikk, tanulmány, mű
math_074_numb_001_002_297-313.pdf Hozzáférés: Csak SZTE egyetemi hálózatról Letöltés (1MB) |
Absztrakt (kivonat)
The notion of //-convexity is a generalized convexity notion with many metrical and combinatorial applications (e.g., in distance geometry, combinatorial geometry, Minkowski geometry, and abstract convexity), and Hconvex sets are simply defined with the help of a finite or infinite system H of unit vectors in Euclidean n-space. In [7], [8], and [9] we investigated non-onesided, so-called M-complete systems of unit vectors and some of their applications in combinatorial geometry. In particular, we established a condition under which the vector (or Minkowski) sum of any two H-convex sets is again H-convex, and conditions for //-separability of H-convex sets. In both cases the notion of M-completeness, defined for the vector systems H , plays the key role. Here we study properties of maximal non-onesided, M - complete vector systems H and H in the unit sphere S n_1 , which means that any non-onesided, M-complete vector system containing them coincides with n_1 . On the other hand, we prove for closed systems, which are symmetric with respect to the origin, that the systems H and H are also universal, i.e., under some natural condition every non-onesided, M-complete vector system distinct from S n _ 1 is contained in H or in H. Some examples illustrate the obtained results.
| Mű típusa: | Cikk, tanulmány, mű |
|---|---|
| Befoglaló folyóirat/kiadvány címe: | Acta scientiarum mathematicarum |
| Dátum: | 2008 |
| Kötet: | 74 |
| Szám: | 1-2 |
| ISSN: | 0001-6969 |
| Oldalak: | pp. 297-313 |
| Nyelv: | angol |
| Kiadó: | Bolyai Institute, University of Szeged |
| Kiadás helye: | Szeged |
| Hivatalos webcím (URL): | http://www.acta.hu |
| Befoglaló mű URL: | http://acta.bibl.u-szeged.hu/38677/ |
| Kulcsszavak: | Matematika |
| Megjegyzések: | Bibliogr.: p. 312-313. ; összefoglalás angol nyelven |
| Szakterület: | 01. Természettudományok 01. Természettudományok > 01.01. Matematika |
| Feltöltés dátuma: | 2016. okt. 15. 14:09 |
| Utolsó módosítás: | 2026. már. 11. 08:24 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/16242 |
 |
Tétel nézet |
