2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78838We define the similarity boundary of a self-similar set and use it to analyze the properties of self-similar sets in the general setting of any complete metric space. The similarity boundary is an attempt at extending the concept of the topological boundary in a way that is consistent with our intuitive understanding of the term boundary. We also show how with the analysis of the similarity boundary, we can restrict ourselves to the space $K$ and disregard the ambient space.14 pagesDynamical SystemsGeneral Topology28A78 54E40 (Primary) 54H15 (Secondary)text