The Similarity Boundary of a Self-Similar Set

Details The Similarity Boundary of a Self-Similar Set The Similarity Boundary of a Self-Similar Set

1999-07-16

arxiv.org/abs/math/9907111v1

Mathematics

Dynamical Systems

14 pages

Scientific paper

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.

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