Zero-dimensional screens and k-imitations in Hilbert space
by
Stoyu Barov
Ball State University
Coauthors: Jan J. Dijkstra, Vrije University - Amsterdam, The Netherlands

Let k be a fixed natural number and B be a closed and convex set in l² with non-empty interior. We construct "minimal" k-imitations C of B, i.e. closed subsets C of B that have the same projections as B onto all k-hyperplanes and that are minimal with respect to dimension. To do this, we apply the following theorem: Let A be a closed set in l² and U be an open neighborhood of A. Then there exists a zero-dimensional closed set F in l² such that F is a subset of U and F is a screen for A, i.e. every line in l² that meets A also meets F.

Date received: January 29, 2003