ITES2001 Fourth Italian-Spanish conference on General Topology and its applications Bressanone, 27-30 June 2001

Dimensional Analysis Some recent results and open problems

Dietrich Kölzow

Matematisches Institut Universität Erlangen-Nürnberg, Germany

Dimensional background of Hilbert’s thirteenth problem (Menger’s and Noebeling’s dimensionally universal spaces; Sternfeld’s characterization of topological dimension by superposition of functions and measures, based on the Theorem of Arnold-Kolmogorov-Ostrand).

Fractalization and chaotization by re-metrization (Zaydler’s and Zuehlke’s results on the set of paper-folding sequences).

Independency of topological, Hausdorff, and Fourier dimension (Bluhm’s construction of sets with pre-assigned dimensions, based on the results of Besicovitch, Jarnik, Kahane, and Kaufman).