Abstract

In this paper we present some new properties of the metric dimension defined by Bouligand in 1928 and prove the following new projection theorem: Let dim_b(A−A) denote the Bouligand dimension of the set A−A of differences between elements of A. Given any compact set A⊆ R^N such that dim_b(A−A) < m, then almost every orthogonal projection P of A of rank m is injective on A and P|_A has Lipschitz continuous inverse except for a logarithmic correction term.

Authors