  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.
