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 C 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.

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