The orthogonal projection of fractal sets

The research in this Ph.D. thesis focuses on the problem of embedding a fractal subset of a Hilbert space into a finite dimensional space by means of an orthogonal projection. We first consider subsets with finite fractal dimension and then study what happens in the case of finite Bouligand dimension. Work along these lines was initiated by Man¯e. The use of Bouligand dimension in the study of such projections was initiated by Movahedi-Lankarani. Our aim is to obtain more stringent regularity properties for the inverse of the embedding map.