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

A characterization of self similar symbolic spaces

Miguel Angel Sanchez-Granero University of Almeria, Spain

We study relations between generalized fractal structures with ”pieces” homeomorphic to the space and different concepts of self homeomorphic spaces. We will also show that each self similar symbolic space has a natural fractal structure, and we will justify the name of fractal structure. Finally we will characterize self similar symbolic spaces in terms of fractal structures, and we will use fractal structures in order to obtain a characterization of self similar symbolic spaces in a similar way, in the form, to the definition of classical self similar sets by means of iterated function systems.

Joint work with F.G. Arenas.