Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A selection theorem in metric trees

Authors: A. G. Aksoy and M. A. Khamsi
Journal: Proc. Amer. Math. Soc. 134 (2006), 2957-2966
MSC (2000): Primary 47H04, 47H10, 54H25, 47H09
Posted: May 1, 2006
MathSciNet review: 2231620
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Abstract | References | Similar Articles | Additional Information

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 of a metric tree with convex values has a selection $T: M\rightarrow M$ for which $d(T(x),T(y))\leq d_H(T^*(x),T^*(y))$ for each $x,y \in M$ . Here by we mean the Hausdroff distance. Many applications of this result are given.

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