Published online by Cambridge University Press: 02 October 2002
Let X be a compact, connected subset of a smooth manifold. Suppose that X admits a codimension d lamination, d\ge 2. Let x,y\in X and \epsilon>0. There exists a sequence x=x_0,\dotsc,x_k=y in X such that the sum of the dth powers of the distances between successive points is less than \epsilon. We discuss two proposed applications of this result.