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The Similarity Boundary of a Self-Similar Set

J. E. Keesling·C. Krishnamurthi
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Abstract

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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J. E. Keesling, C. Krishnamurthi. 1999-07-16. The Similarity Boundary of a Self-Similar Set. https://arxiv.org/abs/math/9907111

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