A general theory of self-similarity II: recognition

Details A general theory of self-similarity II: recognition A general theory of self-similarity II: recognition

2004-11-15

arxiv.org/abs/math/0411345v1

Mathematics

Dynamical Systems

28 pages

Scientific paper

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

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