An Effective Carathéodory Theorem
✍ Scribed by Timothy H. McNicholl
- Publisher
- Springer
- Year
- 2011
- Tongue
- English
- Weight
- 387 KB
- Volume
- 50
- Category
- Article
- ISSN
- 1433-0490
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
In 1976, V. Boltyanski introduced the functional md for compact, convex bodies. With the help of this functional, some theorems of combinatorial geometry were derived. For example, the first author obtained a Helly-type theorem, later some particular cases of the Szo kefalvi Nagy problem were resolv
The following theorem is lproved. If the sets VI, . . . , Vn+, CR" and a E fly:: conv Vi, then there exist elements ui E Vi (i = 1, . . . , n + 1) such that a E conv{o,, . . . , un+J. Thii is a generalization of Carathtidory's theorem. By applying this and similar results some open questions are ans