Abstract
In this paper, we show that nonempty closed convex subsets of a metric tree enjoy many properties shared by convex subsets of Hilbert spaces and admissible subsets of hyperconvex spaces. Furthermore, we prove that a set-valued mapping T* of a metric tree M with convex values has a selection T : M → M for which d(T(x), T(y)) ≤ dH(T*(x), T*(y)) for each x, y ε M. Here by dH we mean the Hausdroff distance. Many applications of this result are given.
Original language | British English |
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Pages (from-to) | 2957-2966 |
Number of pages | 10 |
Journal | Proceedings of the American Mathematical Society |
Volume | 134 |
Issue number | 10 |
DOIs | |
State | Published - Oct 2006 |
Keywords
- Hyperconvex spaces
- Metric trees
- Selection theorems