The Similarity Boundary of a Self-Similar Set

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We 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 pages

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Dynamical Systems, General Topology, 28A78 54E40 (Primary) 54H15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/78838

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9907111
 http://arxiv.org/abs/math/9907111

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arXiv