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"... These problems were presented at the Third International Conference on Discrete Metric Spaces, held at CIRM, Luminy, France, 15--18 September 1998. The names of the originators of a problem are given where these are known and different from the presenter of the problem at the conference. Terminolog ..."

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These problems were presented at the Third International Conference on Discrete Metric Spaces, held at CIRM, Luminy, France, 15--18 September 1998. The names of the originators of a problem are given where these are known and different from the presenter of the problem at the conference. Terminology: In a metric space, the point y is between x and z if d(x; y) + d(y; z) = d(x; z). A d-segment is a set of the form hx; zi of points between x and z. A set S is d-convex if, whenever x; z 2 S, then hx; zi ` S. The path metric in a connected graph G is defined by the rule that d(x; y) is the length of the shortest path from x to y. 1. Transformations which preserve d-convexity. Proposed by Petru Soltan. Address: Usm, Faculty of Mathematics, A. Mateevich Str. 60, Kishinev MD2009, Moldova Email: soltan@usm.md Let R n be a real normed space of dimension n, endowed with the metric d(x 1 ; x 2 ) = jjx 1 \Gamma x 2 jj. Problem: Find all affine transformations of R n which preserve d-c...