- Tytuł:
- On Báránys theorems of Carathéodory and Helly type
- Autorzy:
- Behrends, Ehrhard
- Powiązania:
- https://bibliotekanauki.pl/articles/1206023.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Krein-Milman theorem
Helly
Helly-type theorem
Bárány
Carathéodory
RNP - Opis:
- The paper begins with a self-contained and short development of Bárány's theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads as follows: if $C_{n}$, n=1,2,..., are families of closed convex sets in a bounded subset of a separable Banach space X such that there exists a positive $ε_{0}$ with $⋂_{C ∈ C_{n}} (C)_{ε} = ∅$ for $ε < ε_{0}$, then there are $C_{n} ∈ C_{n}$ with $⋂_{n} (C_{n})_{ε} = ∅$ for all $ε < ε_{0}$; here $(C)_{ε}$ denotes the collection of all x with distance at most ε to C.
- Źródło:
-
Studia Mathematica; 2000, 141, 3; 235-250
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł