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Чебышевские компакты на плоскостистатья
- Автор: Алимов А.Р.
- Журнал: Труды Математического института им.В.А.Стеклова РАН
- Номер: 219
- Год издания: 1997
- Издательство: МИАН
- Местоположение издательства: Москва
- Первая страница: 8
- Последняя страница: 26
- Аннотация: Let X be a real linear space and B is a bounded convex subset of X. Consider the distance function ρ B (x,y)=ρ(0,y-x), where ρ(0,x)=ρ(x) is the Minkowski functional relative to B. A subset M⊂X is called: a Chebyshev set relative to ρ B if P M x={y∈M|ρ B (x,y)=ρ B (x,M)} is a single-point set for every x∈X; M is called a sun relative to ρ B if for each point x∉M there is a point y∈P M x such that y∈P M z for every z in the ray initiating at y and containing x. For a two-dimensional linear space X there are found necessary and sufficient conditions for a bounded convex set B⊂X and for a compact subset K of ℝ 2 so that K can be embedded into X as a Chebyshev set or as a sun relative to ρ B . The result answers partially a question posed by S. V. Konyagin.
- Добавил в систему: Алимов Алексей Ростиславович