2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73247This 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.28 pagesDynamical SystemsCategory TheoryGeneral Topologytext