CONVEXITY IN FINITE METRIC-SPACES

A subset S of a metric space (X, d) is called d-convex if for any pair of points x, y is-an-element-of S each point z is-an-element-of X with d(x, z) + d(z, y) = d(x, y) belongs to S. We give some results and open questions concerning isometric and convexity-preserving embeddings of finite metric spaces into standard spaces and the number of d-convex sets of a finite metric space.