A general theory of selfsimilarity II: recognition
Abstract
This paper concerns the selfsimilarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize selfsimilar spaces, or more precisely, universal solutions of selfsimilarity systems. Examples include the standard simplices (selfsimilar by barycentric subdivision) and solutions of iterated function systems. Perhaps surprisingly, every compact metrizable space is selfsimilar in at least one way. From this follow the classical results on the role of the Cantor set among compact metrizable spaces.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2004
 arXiv:
 arXiv:math/0411345
 Bibcode:
 2004math.....11345L
 Keywords:

 Dynamical Systems;
 Category Theory;
 General Topology
 EPrint:
 28 pages