This paper contains several generalizations of the Mazur-Ulam isometric theorem in F \* -spaces which are not assumed to be locally bounded. Let X and Y be two real F \* -spaces, and let X be locally pseudoconvex or δ-midpoint bounded. Assume that a operator T maps X onto Y in a δ-locally 1/2 i -iso
On Generalizations of Radon's Theorem and the Ham Sandwich Theorem
✍ Scribed by Helge Tverberg; Siniša Vrećica
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 211 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
✦ Synopsis
We raise a conjecture which would generalize Radon's theorem and would provide combinatorial proof for the result from [7], which generalizes Rado's theorem on general measure and the Ham sandwich theorem.
We prove that the conjecture holds in several particular cases.
📜 SIMILAR VOLUMES
The work is devoted to the calculation of asymptotic value of the choice number of the complete r-partite graph K m \* r = K m,. ..,m with equal part size m. We obtained the asymptotics in the case ln r = o(ln m). The proof generalizes the classical result of A.L. Rubin for the case r = 2.
respectively for the spectrum and the Weyl spectrum of T ; moreover, Weyl's Ž . theorem holds for f T q F if ''dominant'' is replaced by ''M-hyponormal,'' where F is any finite rank operator commuting with T. These generalize earlier results for hyponormal operators. It is also shown that there exis