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The Similarity Boundary of a Self-Similar Set

Dynamical Systems 2007-05-23 v1 General Topology

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 KK and disregard the ambient space.

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Cite

@article{arxiv.math/9907111,
  title  = {The Similarity Boundary of a Self-Similar Set},
  author = {J. E. Keesling and C. Krishnamurthi},
  journal= {arXiv preprint arXiv:math/9907111},
  year   = {2007}
}

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14 pages