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Convexity of Balls in Gromov--Hausdorff Spaceстатья
- Автор: Klibus Daria P.
- Сборник: ArXiv.org e-Print
- Серия: Series arxive "math"
- Аннотация: In this paper we study the space M of all nonempty compact metric spaces considered up to isometry, equipped with the Gromov-Hausdorff distance. We show that each ball in M with center at the one-point space is convex in the weak sense, i.e., every two points of such a ball can be joined by a shortest curve that belongs to this ball, however, such a ball is not convex in the strong sense: it is not true that every shortest curve joining the points of the ball belongs to this ball. We also show that a ball of sufficiently small radius with center at a space of general position is convex in the weak sense.
- Добавил в систему: Клибус Дарья Петровна